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x implies y

Part one seems fairly easy (I might be setting my self up for a nice foot-flavored meal though):

If the white triangle is frobby, then the author is thinking of either the color white or the shape triangle, but not both... That means that he is also thinking of either the color black or the shape circle but not both, making the black circle also frobby.

Of the other two shapes, one will have both the correct shape and color, and the other will have neither, so they are both not frobby.


For part two,  you definitely need to turn over the card with a 5, to see that the letter on the other side is a vowel. You do NOT need to turn over the E card, because the rules of the problem say nothing about vowels  having odd numbers on the other side. However, you will need to turn over the F card, to make sure that the number on the other side is NOT odd, since that would disprove the rule.

So the answer is 2 cards : 5 and F

levik
Friday, February 08, 2002

Four cards: 2 5 F E
Rule: card with an odd number on one side must have a vowel on the other.
Solution:  3 cards must be turned over to prove the rule.  The cards are 5, F, and E

2:  even number, leave alone; no even rule
5:  Odd number, must verify other side is a vowel
F:  Consonant, must verify other side is not odd
E:  Vowel, must verify other side IS odd

blekros
Friday, February 08, 2002

levik is correct, blekros is not

This may help

odd implies vowel

therefore, by the contrapositive rule

not vowel implies not odd

No other implications can be drawn.  So you need to check 5 since it implies a vowel is on the other side and F since it implies the number on the other side is not odd.

Roy Pollock
Friday, February 08, 2002

Sorry, I knew I screwed it up the minute I posted.

However, not knowing anything about logic, I take the following statements:

odd implies vowel
not vowel implies not odd

to mean:

odd=vowel
consonent=even

The one-to-one relationships map the entire domain.
You must flip them all over.

2 5 F E 

blekros
Friday, February 08, 2002

Implication is not the same as equality.

Thats why "x implies y" is written as "x => y"
and "x is equivalent to y" is written "x <> y"
(in one of far too many ways)

x implies y means that if x is true, y must be true.  It gives no information about y if x is false.

If x implies y and y implies x, then x <> y, or x = y, or x is y, whatever you prefer.

The fact that implication is only one directional is why you only need to turn over half the cards--The other visible symbols are only at the receiving end of the implications and don't matter.

Roy Pollock
Friday, February 08, 2002

The second question did not specify base 10. If the numbers are in hex you have to turn over the F too and you only have to turn over the E if it counts as a vowel as well as a number. :-)

Sidney Markowitz
Sunday, February 10, 2002

Aargh, I hit the wrong key and posted before I was done editing. What I *meant* to point out is the interesting result that the answer to part 2 is the same if the numbers are in hex, since you have to turn over 5 and F as the odd numbers.

By the way, this is also making the assumption that the statement that all cards have a number on one side and a letter on the other should not be questioned. Otherwise you have to turn over the 2 to verify that there is not an odd number on the other side.

You would not have to turn over the E, since even if the other side was a letter it would violate the initial statment but would not violate the rule.

Sidney Markowitz
Sunday, February 10, 2002

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