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x implies y


Think of a quadrant divided up by color and shape. WRT any one quadrant, the frobby quadrants are the ones that share an edge. The non-frobby quadrant is the opposite/catty-cornered one that touches only at the origin. (This is like a True/False graph of the XOR operator.)

So no matter what we label the axes the graph will be of the form:

FR NF      NF FF
NF FR      FR NF
        OR

WRT any quadrant, the adjacent quadrants have the reverse frobbiness and the opposite quadrant has the same frobbiness.

Given that the white triangle is frobby the "adjacent" shapes (white circle and black triangle) must be non-frobby. The "opposite" shape (black circle) must be frobby.

We can't tell which of the two non-frobby shapes is the "thought of" shape without further information.


Part II

You have to know that for x->y the only falsifying condition is if x is true and y is false. The claim is "a card with an odd number on one side must have a vowel on the other." An odd number implies a vowel. So to prove the rule wrong we must find a card with an odd number on one side and a consonant on the other. To prove the rule true we must exhaust the possible falsifying cases.

You have to turn over the 5, because it might have a consonant on the other side. You have to turn over the F, because it might have an odd number on the other side.

You don't have to turn over the 2 or the E, because the rule would still hold regardless of what was on the backs of those cards.

Alex Joneth
Tuesday, July 20, 2004

I don't think you need to turn over the 5; the condition only says "a card with an odd number on one side must have a vowel on the other", which says nothing about whether it's legal for a card with a consonant to have an odd number on the back. So you only need to turn over the E.

James Harlow
Monday, October 04, 2004

36|

59+2+92+9
Wednesday, October 13, 2004

No, you definitely need to turn over both the 5 and the F.

"a card with an odd number on one side must have a vowel on the other" and
"a card with no vowel on one side cannot have an odd number on the other"

are identical rules.

(Actually, usually people have trouble with the "F"...the "5" is pretty straightforward: A card with an odd number on one side must have a vowel on the back. 5 is an odd number, so that card had better have a vowel on the back.)

Avrom Roy-Faderman
Thursday, October 14, 2004

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