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Quote:
And, the red herring "not a" (which does not prove "not b") is there to tempt the examinee.
Not to mention "b" (which does not prove "a").
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" Four cards are presented: A, B, 4, and 7. There is a letter on one side of each card and a number on the other side. Which card(s) must you turn over to determine whether the following statement is false? "If a card has a vowel on one side, then it has an even number on the other side."OptionsA+ odd... yes the statement is false. A+ even...no you can't prove the statement false. B+ odd...not germane B+ even...not germane 4+ vowel...not germane 4+ consonant...not germane 7+ vowel... yes, the statement is false7+ consonant...not germane. Only one of the four cards MUST be turned over to prove the statement false. And the answer is "A". Not "A" and then maybe "7". Only the "A" has to be turned over; even if turning over the "7" is needed for the proof. Geez! I'd like to sell you guys a used car and a garage in the swamp. 
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Or either "7" and then, maybe, "A", one. You got no call to claim that "A" is any way more special than "7".
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Oh yes I do, Faldage, but I'm in my cups tonight so I'll explain it to you monyanna*.  * " phonetically speaking."
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On second thought I might forget my incisive logic in the fog of the grey dawn of morning so I'll regale you with it now. as follows... Listen closely..."IF" (the man says) "the vowel is ..." Get it? The proposition (and question) is based upon that contention. Really Faldage, you MUST stop making up your own rules. 
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And the logical equivalent* is "If the number is not ..."
*The logical contrapositive, to be specific.
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Quote:
Listen closely..."IF" (the man says) "the vowel is ..."
Get it? The proposition (and question) is based upon that contention.
Really Faldage, you MUST stop making up your own rules.
The proposition is "If a card has a vowel on one side, then it has an even number on the other side." (BTW, that is a direct copy and paste. The phrase "the vowel is" does not occur even in the discussion much less the statement of the problem.)
"On one side" means if the card has a vowel on either side, not just the side that's showing. It does matter what's on the other side of the 7.
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Don't be like Faldage who would rather drink muddy water than admit that he is wrong. Instead listen carefully this one last time and you will become a more knowledgable man even if you are a woman. [Four cards are presented: A, B, 4, and 7. There is a letter on one side of each card and a number on the other side. Which card(s) must you turn over to determine whether the following statement is false? If a card has a vowel on one side, then it has an even number on the other side.]Ok, last chance... The question requires that you find a card to turn over that has a vowel on one side. Only card "A" has a vowel showing of the four. Card "4" (an even number) can sport any letter and still be consistant with the statement in question. Turning over card "4" can't prove or disprove the statement unless card "A" has been turned over first. Therefore you MUST turn over card "A" first in order to prove or disprove the statement. As in... Which card(s) must you turn over to determine whether the following statement is false?See that wasn't so hard, now was it?
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Oh, I don't mind admitting that I'm wrong WHEN I'M WRONG.
Assuming only these four cards you just might could turn card A over and find an even number. You haven't proven the hypothesis false. If you then turn over card 7 and find a vowel, then and only then have you proven the hypothesis false. And in this case turning over just the 7 card will be sufficient to prove it false and you can take your A card and paint it green for all I care.
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Quote:
If a card has a vowel on one side, then it has an even number on the other side
If the 7 card has A, E, I, O, or U on the side that you can't see then there is a card which has a vowel on one side and an odd number on the other side which makes the statement false.
If the problem stated that these are the fronts of the cards and the statement said "If a card has a vowel on the front, then it has an even number on the back" you would be right, but it doesn't say that. Both sides are equally sides of the card
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