Conditional Reasoning, Skills in Deduction & Forming Proper Conclusions in this JFK Thing of Ours

[Glenn Nall]

You have not understand what if, then means, if you said earlier, if or then.

That's not how it works.

I'm flat tired of defending myself to you, Ken. I was trying to have a little intellectual fun and stimulate some thinking, and you've taken all the fun out of this.

The irony is that NO ONE else has had any cognitive problems with the wording, or the conditions, or anything. Only you.

TWO people have got the right answer already, Mark is as close as he can be, John's reasoning is perfect, Jon's almost there, others have bounced all around the answer - NONE OF THEM seem to have been confused about very much and decided to blame the test.

I'm gonna go address your insinuations and assertions, then I'm going to post the answer to the tests.

[Glenn Nall]

The K card can be discarded. The other side of the K card could be an even number, or could be an odd number. Discard the K card.

The other side of the K card could be a vowel.

RIGHT.

There's nothing in Glenn's problem statement that excludes this possibility.

RIGHT.

If there is a vowel on the other side of the K card, then the proposition is proved false.

WRONG.

You cannot discard the K card.

[Glenn Nall]

The K card can be discarded. The other side of the K card could be an even number, or could be an odd number. Discard the K card.

The other side of the K card could be a vowel. There's nothing in Glenn's problem statement that excludes this possibility. If there is a vowel on the other side of the K card, then the proposition is proved false. You cannot discard the K card.

If there is a vowel on the other side of the K card, then the proposition is proved false.

If there is a vowel on the reverse side you wouldn't know it because you have not seen it since you can't turn over a card that does not fit the first qualifier, If a vowel......then

I asked once before - now again. WHERE DO YOU GET THIS IDEA? That is NOT how if, then works.

IF you would open your mind to the possibility of being incorrect, THEN you might learn something.

IF I bang my knee - knowing that there's a statement following, this means WHEN I bang my knee, whenever I bang my knee, at any point in time that I bang my knee - (that is the condition; UNDER THE CONDITION being that I bang my knee), THEN I will scream. at that time I will scream - the RESPONSE to the stimulus of me having banged my knee is my scream.

It is not open to debate, there's no maybe I will scream, it does not imply that a scream, or a whimper, is a possibility. It is stated as an absolute that IF I bang my knee THEN I will scream.

according to this fundamental precept, it also goes that I will always scream if I bang my knee.

And if the rule is that there is an even number on the reverse (the word side is implied. In the English language, many words in a sentence are left to implication, or they are 'understood') of a vowel, then, YES, there will ALWAYS be an even number opposite a lvowel.

Edited August 13, 2015 by Glenn Nall

[Glenn Nall]

This is an awesome puzzle. My answer is that you have to turn over everything but the 4. Some people are making the assumption that each card must have a letter on one side and a number on the other. That's not a given. The "K" could have a vowel on the other side. It's irrelevant what's on the other side of the 4 because if it's a vowel it confirms the proposition but if it's not it doesn't violate the proposition. You only need to look for falsifying evidence .

in fact, i think that it IS the case that each card contains both letter and number - in another version of this it so states. but this would not effect (affect?) the answer.

if you turn over K, you learn the same thing regardless what's on the other side - even or odd, letter or number, it neither proves nor disproves the postulate.

It most certainly matters if you state beforehand that each card must have a letter on one side and a number on the other. If that is not a given, then you have to turn over the K because it might have a vowel on the other side. If that is a given then you only have to turn over the E and the 7.

Also, some people are making the mistake of thinking that the puzzle makes a distinction between the top side and the bottom side. The postulate is "if a card has a vowel on one side, then it has an even number on the other side", it doesn't say "if a card has a vowel on the top side, then it has an even number on the bottom side". So you can't just check the card that has a vowel on the top.

You know what, you're right.

I'm going to post the test in its entirety along with the links to it and it's other brother further...

They are both the same test, with a variation, and I may have been mistaken in saying that it doesn't matter.

Either way, THIS ONE does NOT say that one side has to be a letter and one side a number. It's posted in its original form, and I think I told someone else that I may have been mistaken in saying that that's not a safe assumption, but it turns out that you are right. That's not a safe assumption. Good catch.

No harm with this test, tho. It stands fine as its presented.

[Kenneth Drew]

let me ask this simple question Glenn First let me make a general statement. There is one house on my street that has a yellow door. There are 4 houses on my street that have 3 bathrooms. All houses in my neighborhood that have a yellow door have 3 bathrooms. with that in place. you may visit all the houses in my neighborhood, if a house has a yellow door, you may enter that house to see if it is one that has 3 bathrooms. Now the question, how many houses can you enter in my neighborhood to see if it has 3 bathrooms?

[Kenneth Drew]

You have not understand what if, then means, if you said earlier, if or then.

That's not how it works.

I'm flat tired of defending myself to you, Ken. I was trying to have a little intellectual fun and stimulate some thinking, and you've taken all the fun out of this.

The irony is that NO ONE else has had any cognitive problems with the wording, or the conditions, or anything. Only you.

TWO people have got the right answer already, Mark is as close as he can be, John's reasoning is perfect, Jon's almost there, others have bounced all around the answer - NONE OF THEM seem to have been confused about very much and decided to blame the test.

I'm gonna go address your insinuations and assertions, then I'm going to post the answer to the tests.

I'm flat tired of defending myself to you, Ken. I was trying to have a little intellectual fun and stimulate some thinking, and you've taken all the fun out of this.

And that's the way I've taken it. I have not intended to get you all bent out of shape just because of a game. I have tried to take it all as fun. I will be interested to see the 'official' answer because obviously i'm not gonna agree with it. Apparently IF and THEN, means something different to me than to the puzzle writer. I believe that it is likely that the problem is going to be that the meaning of IS is something orther than IS.

[Glenn Nall]

Glenn Nall:

You are shown a set of four cards placed on a table, each of which has a number on one side and a letter on the other side... Which card(s) must you turn over in order to test the truth of the proposition that if a card shows an even number on one face, then its opposite face is a vowel?

IT IS NOT STIPULATED THAT EACH HAS A NUMBER AND A LETTER. I LATER SUGGESTED THAT IT MIGHT BE SO WHEN SOMEONE ELSE ASSUMED THAT, BUT AS JOHN HAS JUST POINTED OUT, THAT'S WRONG.

Another shot (pun intended).

If the E card is turned over, and the other side has an even number, the proposition is shown to be true in one case. It is not shown to be true universally.

EXACTLY. AND AT THIS POINT ANOTHER NEEDS TO BE TURNED...

If the E card is turned over, and the other side has an odd number, the proposition is shown to be false in one case. It is not shown to be false universally.

MISTAKE. READ THE STATEMENT IN AT ITS FACE VALUE, 'If vowel, then even'. The premise is broken in these four cards' universe. Once it's false, it's false.

The K card can be discarded. The other side of the K card could be an even number, or could be an odd number. Discard the K card.

The 4 card can be discarded. The other side of the 4 card could be a vowel or could be a consonant. Discard the 4 card.

The 7 card is key, in a sense. The other side of the 7 card could be a vowel (proposition not proved universally) or could be a consonant (nothing proved).

RIGHT, RIGHT, WRONG.

IF THE 7 HAS A VOWEL ON THE REVERSE, THEN THE STATEMENT IS PROVED FALSE. THAT'S YOUR ANSWER.

E and 7.

Glenn,

I believe you've asked a question that cannot be answered. Cannot be answered because of lack of definition.

Your question is:

Which card(s) must you turn over in order to test the truth of the proposition that if a card shows an even number on one face, then its opposite face is a vowel?

AS I ASKED KEN, WHAT'S your DEFINITION OF 'VOWEL'? I DIDN'T KNOW THERE WERE OPTIONS. ARE YOU OFTEN WONDERING WHEN IN DISCUSSION WITH THE GIRL AT BURGER KING WHAT HER DEFINITION OF A VOWEL IS SO THAT SHE UNDERSTANDS YOUR ORDER?

You do not define "truth of the proposition". You present four cases. What if the proposition is false in the four cases you present but true in a fifth case? For example, in the fifth case of a card having "a" on one side and "2" on the other.

How many cases may we consider?

HOW VERY INTERESTING. THE EXERCISE IS ONE CASE. IT BEGINS 'HAVE FOUR CARDS BELOW'... HOW MANY CARDS REFRS TO THE SET OF FOUR CARDS. THERE IS NO 5TH.

If you maintain the universe of all cases is composed of the four cases you present, I have to ask, must the proposition hold true (i.e., not be contradicted) in each of the four cases you present? Or must it be true in only one of the cases you present?

IT SEEMED CLEAR TO ME, AND TO ALL THE OTHERS WHO TOOK THIS TEST OVER THE PAST FIVE DECADES. WHAT UNIVERSE? YOU HAVE FOUR CARDS, YOU HAVE A STATEMENT. PROVE THE STATEMENT TRUE OR FALSE.

HOW HARD IS THAT? (ASK KEN.)

I'm fascinated by your diary. It poses a set of facts, and then asks a question about the facts. The issue for me is whether your question makes sense.

RIGHT.

[Kenneth Drew]

This is an awesome puzzle. My answer is that you have to turn over everything but the 4. Some people are making the assumption that each card must have a letter on one side and a number on the other. That's not a given. The "K" could have a vowel on the other side. It's irrelevant what's on the other side of the 4 because if it's a vowel it confirms the proposition but if it's not it doesn't violate the proposition. You only need to look for falsifying evidence .

The "K" could have a vowel on the other side. No it can't. Vowels have even numbers on the back side, not other letters.

this is one of the errors that some people are making, and the point of the exercise:

Vowels have even numbers on the back side, not other letters.

the condition is simply this: if it's a vowel, then the other side is an even number. and nothing else.

there is nothing that states, or implies, that:

consonants cannot have an even number, or another consonant, or an odd number, or a naked - goat - on the other side.

there is nothing that states, or implies, that:

a person cannot turn over any card unless it shows X or until the "if" is satisfied.

turning E over does one of two things: it proves the statement TRUE - SO FAR - if the other side is an EVEN #, --- OR --- it proves it false right away if there is NOT an EVEN number there.

the mission is to prove the statement true or false with the least amount of turns with the given set of cards.

so if you turn E and there's a 2, -> so far, the statement is true. if you turn K, then you have to ask yourself what is proven under the ensuing situation. if there's a 3, then what? if there's a 4, then what? if there's a Z, then what? if there's a nude goat, then what? so is it necessary to turn K?

and so on and so forth...

the condition is simply this: if it's a vowel, then the other side is an even number. and nothing else. Ok.

there is nothing that states, or implies, that: Yes there is: the very first condition is If it's a vowel it has an even number on the back side.

Remember this sentence from post 1: The condition is now established (true): 'If a card has a vowel on one side, then it has an even number on the other side.'

I interpret that as if a card has a vowel on one side, then it has an even number on the other side.

Edited August 13, 2015 by Kenneth Drew

[Glenn Nall]

You have not understand what if, then means, if you said earlier, if or then.

That's not how it works.

I'm flat tired of defending myself to you, Ken. I was trying to have a little intellectual fun and stimulate some thinking, and you've taken all the fun out of this.

The irony is that NO ONE else has had any cognitive problems with the wording, or the conditions, or anything. Only you.

TWO people have got the right answer already, Mark is as close as he can be, John's reasoning is perfect, Jon's almost there, others have bounced all around the answer - NONE OF THEM seem to have been confused about very much and decided to blame the test.

I'm gonna go address your insinuations and assertions, then I'm going to post the answer to the tests.

I'm flat tired of defending myself to you, Ken. I was trying to have a little intellectual fun and stimulate some thinking, and you've taken all the fun out of this.

And that's the way I've taken it. I have not intended to get you all bent out of shape just because of a game. I have tried to take it all as fun. I will be interested to see the 'official' answer because obviously i'm not gonna agree with it. Apparently IF and THEN, means something different to me than to the puzzle writer. I believe that it is likely that the problem is going to be that the meaning of IS is something orther than IS.

Again ... you'll note that no one else had problems with the wording or design of the test. Only you. The other questions were legitimate concerns of clarity. Yours, not so much.

You never once wondered who got it right, or how they did.

You've failed to reply to my questions.

Your test does not remotely resemble this exercise in logic (yours is a test of reading and comprehension). Start your own thread. I'll answer it later, but to answer it now would be to allow you to change direction from the solution to this - these - problems.

[Glenn Nall]

This is an awesome puzzle. My answer is that you have to turn over everything but the 4. Some people are making the assumption that each card must have a letter on one side and a number on the other. That's not a given. The "K" could have a vowel on the other side. It's irrelevant what's on the other side of the 4 because if it's a vowel it confirms the proposition but if it's not it doesn't violate the proposition. You only need to look for falsifying evidence .

The "K" could have a vowel on the other side. No it can't. Vowels have even numbers on the back side, not other letters.

this is one of the errors that some people are making, and the point of the exercise:

Vowels have even numbers on the back side, not other letters.

the condition is simply this: if it's a vowel, then the other side is an even number. and nothing else.

there is nothing that states, or implies, that:

consonants cannot have an even number, or another consonant, or an odd number, or a naked - goat - on the other side.

there is nothing that states, or implies, that:

a person cannot turn over any card unless it shows X or until the "if" is satisfied.

turning E over does one of two things: it proves the statement TRUE - SO FAR - if the other side is an EVEN #, --- OR --- it proves it false right away if there is NOT an EVEN number there.

the mission is to prove the statement true or false with the least amount of turns with the given set of cards.

so if you turn E and there's a 2, -> so far, the statement is true. if you turn K, then you have to ask yourself what is proven under the ensuing situation. if there's a 3, then what? if there's a 4, then what? if there's a Z, then what? if there's a nude goat, then what? so is it necessary to turn K?

and so on and so forth...

the condition is simply this: if it's a vowel, then the other side is an even number. and nothing else. Ok.

there is nothing that states, or implies, that: Yes there is: the very first condition is If it's a vowel it has an even number on the back side.

Remember this sentence from post 1: The condition is now established (true): 'If a card has a vowel on one side, then it has an even number on the other side.'

There is a colon after 'nothing that state or imiles that:' meaning that what follows is the object of the sentence. The sentence doesn't end with 'that:'.

There's nothing that states that consonants cannot have ...

There's nothing that states that a person cannot turn over...

The condition, WHICH IS WHAT NEEDS TO BE PROVED TRUE OR FALSE, is now established that...

Did you forget about the challenge part of this?

[Glenn Nall]

http://changingminds.org/explanations/decision/conditional_reasoning.htm

If...then...

Conditional reasoning is based on an 'if A then B' construct that posits B to be true if A is true.

Note that this leaves open the question of what happens when A is false, which means that in this case, B can logically be either true or false.

Conditional traps

A couple of definitions: In the statement 'If A then B', A is the antecedent and B is the consequent.

You can affirm or deny either the antecedent or consequent, which may lead to error.

Denying the consequent

Denying the consequent means going backwards, saying 'If B is false, then A must also be false.' Thus if you say 'If it is raining, I will get wet', then the trap is to assume that if I am not getting wet then it is not raining.

Denying the antecedent

Denying the antecedent is making assumptions about what will happen if A is false. Thus if you say 'If it is raining, I will get wet' and is not raining, I might assume that I will not get wet. But then I could fall in the lake.

Affirming the consequent

This is making assumptions about A if B is shown to be true. Thus if I make the statement 'If it is raining, I will get wet', then if I am getting wet it does not mean that it is raining.

The card trap

A classic trap was used by Wason and Johnson-Laird (1972) to show how

Four cards are laid out as below:

E K 4 7

The conditional statement is now given: 'If a card has one vowel on one side, then it has an even number on the other side.'

The question is to decide which are the minimum cards that need to be turned over to prove that the conditional statement is true.

More than half of people questioned said E and 4.

To affirm the antecedent, E is correct. E is a vowel and thus should have an even number on the other side. If there was an odd number on the other side, the statement would be false, so E must be turned over to check for this.

But choosing 4 is affirming the consequent. Even though 4 is even, it can have a vowel or consonant on the other side and the statement is not falsified.

Only 4% said E and 7. The 7 could deny the consequent and hence must be checked. If there was a vowel on the other side, the statement would be false.

So what?

Be careful about if-then statements, both in your own use and in those that others use. It does, of course also mean that you can make statements that are logically false and few people will challenge you.

/////

https://en.m.wikipedia.org/wiki/Wason_selection_task

Wason Selection Task

Each card has a number on one side, and a patch of color on the other. Which card(s) must be turned over to test the idea that if a card shows an even number on one face, then its opposite face is red?

The Wason selection task (or four-card problem) is a logic puzzle devised by Peter Cathcart Wason in 1966.[1][2][3] It is one of the most famous tasks in the study of deductive reasoning.[4] An example of the puzzle is:

You are shown a set of four cards placed on a table, each of which has a number on one side and a colored patch on the other side. The visible faces of the cards show 3, 8, red and brown. Which card(s) must you turn over in order to test the truth of the proposition that if a card shows an even number on one face, then its opposite face is red?

A response that identifies a card that need not be inverted, or that fails to identify a card that needs to be inverted, is incorrect. The original task dealt with numbers (even, odd) and letters (vowels, consonants).

The importance of the experiment is not in justifying one answer of the ambiguous problem, but in demonstrating the inconsistency of applying the logical rules by the people when the problem is set in two different contexts but with very similar connection between the facts.

[Kenneth Drew]

You have not understand what if, then means, if you said earlier, if or then.

That's not how it works.

I'm flat tired of defending myself to you, Ken. I was trying to have a little intellectual fun and stimulate some thinking, and you've taken all the fun out of this.

The irony is that NO ONE else has had any cognitive problems with the wording, or the conditions, or anything. Only you.

TWO people have got the right answer already, Mark is as close as he can be, John's reasoning is perfect, Jon's almost there, others have bounced all around the answer - NONE OF THEM seem to have been confused about very much and decided to blame the test.

I'm gonna go address your insinuations and assertions, then I'm going to post the answer to the tests.

I'm flat tired of defending myself to you, Ken. I was trying to have a little intellectual fun and stimulate some thinking, and you've taken all the fun out of this.

And that's the way I've taken it. I have not intended to get you all bent out of shape just because of a game. I have tried to take it all as fun. I will be interested to see the 'official' answer because obviously i'm not gonna agree with it. Apparently IF and THEN, means something different to me than to the puzzle writer. I believe that it is likely that the problem is going to be that the meaning of IS is something orther than IS.

Again ... you'll note that no one else had problems with the wording or design of the test. Only you. The other questions were legitimate concerns of clarity. Yours, not so much.

You never once wondered who got it right, or how they did.

You've failed to reply to my questions.

Your test does not remotely resemble this exercise in logic (yours is a test of reading and comprehension). Start your own thread. I'll answer it later, but to answer it now would be to allow you to change direction from the solution to this - these - problems.

You never once wondered who got it right, or how they did. LOL, you said I got it wrong. there have been two answers 1 and 2 and you said two got it right, so obviously the two that said 2 got it right. Doesn't that tell me?

You've failed to reply to my questions. I believe I answered every one.

This is/was the 'original' question/statement:

From post 1: The condition is now established (true): 'If a card has a vowel on one side, then it has an even number on the other side.'

Has now been changed to:

in post 100: The condition, WHICH IS WHAT NEEDS TO BE PROVED TRUE OR FALSE, is now established that..

So I hope you can see that in post one you stated: that the condition is now established (true)

and now in post 100 you are saying that "the condition, which is what needs to be proved true or false.

So i guess that when you state that a condition which has been established to be true now becomes one that has to be proved to be true or false it's going to cause an entirely different answer.

As I said at some point above, I think the way the question was asked (not by you, but the originator) is what caused the misunderstanding.

[John Dolva]

I read http://www.psychologyinaction.org/2012/10/07/classic-psychology-experiments-wason-selection-task-part-i/and I think I understand a bit more but not really. Perhaps the answer for me lies in understanding thematic, semantic. I'll ponder on it, maybe the answer will come to me in time.

[Kenneth Drew]

I don't mean to annoy anyone - i do feel that this is an appropriate (and fun) topic in each of us understanding more what's involved in the conclusion forming process which can either lead to errors in deduction or to progress in our pursuit of accuracy and truth in the solution.

one of the real reasons i'm into this thing so much is my passion for 'problem solving,' and i'm sure that's the case for many of ya'll. so these kinds of things are fun, and good for our brains (which we need to solve this thing!)

i'm just pasting in this little bit of text and this quick test i found (that I failed) without the answer. if any of you have seen it already, which is very likely, please don't publish the answer, or cheat.

so, check it out:

If...then...

Conditional reasoning is based on an 'if A then B' construct that posits B to be true if A is true.

Note that this leaves open the question of what happens when A is false, which means that in this case, B can logically be either true or false.

Conditional traps

A couple of definitions: In the statement 'If A then B', A is the antecedent and B is the consequent.

You can affirm or deny either the antecedent or consequent, which may lead to error.

Denying the consequent

Denying the consequent means going backwards, saying 'If B is false, then A must also be false.' Thus if you say 'If it is raining, I will get wet', then the trap is to assume that if I am not getting wet then it is not raining.

Denying the antecedent

Denying the antecedent is making assumptions about what will happen if A is false. Thus if you say 'If it is raining, I will get wet' and is not raining, I might assume that I will not get wet. But then I could fall in the lake.

Affirming the consequent

This is making assumptions about A if B is shown to be true. Thus if I make the statement 'If it is raining, I will get wet', then if I am getting wet it does not mean that it is raining.

The card trap

A classic trap was created some years ago;

Four cards are laid out as below:

The condition is now established (true): 'If a card has a vowel on one side, then it has an even number on the other side.'

The problem is to decide which are the minimum cards that need to be turned over to prove that the conditional statement is true. How many and which card(s)?

OR (these are the same challenges, just worded a little differently):

Which card(s) must you turn over in order to test the truth of the proposition that if a card shows a vowel on one face, then its opposite face is an EVEN number?

Discuss it among yourselves...

The card trap

A classic trap was created some years ago;

Four cards are laid out as below:

The condition is now established (true): 'If a card has a vowel on one side, then it has an even number on the other side.'

The problem is to decide which are the minimum cards that need to be turned over to prove that the conditional statement is true. How many and which card(s)?

OR (these are the same challenges, just worded a little differently):

Which card(s) must you turn over in order to test the truth of the proposition that if a card shows a vowel on one face, then its opposite face is an EVEN number?

Discuss it among yourselves...

The card trap

A classic trap was used by Wason and Johnson-Laird (1972) to show how

Four cards are laid out as below:

E K 4 7

The card trap

A classic trap was created some years ago;

Four cards are laid out as below:

1The conditional statement is now given: 'If a card has one vowel on one side, then it has an even number on the other side.'

2The condition is now established (true): 'If a card has a vowel on one side, then it has an even number on the other side.'

3The question is to decide which are the minimum cards that need to be turned over to prove that the conditional statement is true.

4The problem is to decide which are the minimum cards that need to be turned over to prove that the conditional statement is true. How many and which card(s)?

More than half of people questioned said E and 4.

To affirm the antecedent, E is correct. E is a vowel and thus should have an even number on the other side. If there was an odd number on the other side, the statement would be false, so E must be turned over to check for this.

But choosing 4 is affirming the consequent. Even though 4 is even, it can have a vowel or consonant on the other side and the statement is not falsified.

Only 4% said E and 7. The 7 could deny the consequent and hence must be checked. If there was a vowel on the other side, the statement would be false.

So what?

Be careful about if-then statements, both in your own use and in those that others use. It does, of course also mean that you can make statements that are logically false and few people will challenge you.

The card trap

A classic trap was used by Wason and Johnson-Laird (1972) to show how

Four cards are laid out as below:

E K 4 7

The conditional statement is now given: 'If a card has one vowel on one side, then it has an even number on the other side.'

The question is to decide which are the minimum cards that need to be turned over to prove that the conditional statement is true.

More than half of people questioned said E and 4.

To affirm the antecedent, E is correct. E is a vowel and thus should have an even number on the other side. If there was an odd number on the other side, the statement would be false, so E must be turned over to check for this.

But choosing 4 is affirming the consequent. Even though 4 is even, it can have a vowel or consonant on the other side and the statement is not falsified.

Only 4% said E and 7. The 7 could deny the consequent and hence must be checked. If there was a vowel on the other side, the statement would be false.

So what?

Be careful about if-then statements, both in your own use and in those that others use. It does, of course also mean that you can make statements that are logically false and few people will challenge you.

Okay, I posted it the way you originally posted, then I posted the way you just posted it which is an exact copy from the original source.

down under the 4 cards, there are alternating color lines.

Line 2 in black is the way you published it in post 1

Line 1 in red is the way you just posted it in 100

Line 4 in black from post 1

line 3 in red from post 100

Now you can say they are 'exactly' the same thing.

but clearly line 2 says that the condition is established true.......that if it's a vowel then back side is even

whereas line 1 says it's conditional and to be determined.

In one case if it is established as true then it is not still to be determined if it is true or not.

End of discussion. Question was stated incorrectly to get the answer desired..

Edited August 13, 2015 by Kenneth Drew

[Robert Prudhomme]

Glenn

Are you saying the correct answer is E and 7?