proof: Consider tokens that have some letter written on one

[shivers20]

Consider tokens that have some letter written on one side and some integer written on the other, in unknown combinations. The tokens are laid out, some with letter side up, some with number side up. Explain which tokens must be turned over to determine, with the minimum number of flips, whether these statements are true:

a) If the letter side is a vowel, then the number side is odd.

b) The letter side is a vowel if and only if the number side is even.

I am not really sure what they are asking but here goes,

Construct a truth table.

vowel ---->odd
vowel<--->even

I am stumped.

 

[shivers20]

Am I on the right track? aCCORDING TO MY TRUTH TABLES:

if A then B would give me a final result of T,F,T,T

A if and only if B would give me a final result of T,F,F,T

 

[pka]

Consider tokens that have some letter written on one side and some integer written on the other, in unknown combinations. a) If the letter side is a vowel, then the number side is odd.
b) The letter side is a vowel if and only if the number side is even.

For the part (a) because there is only one case we cannot allow, T->F, you need to turn over only the vowels.

For the part (b), however, you need to turn over any vowel and any odd number.

 

[shivers20]

Consider tokens that have some letter written on one side and some integer written on the other, in unknown combinations. a) If the letter side is a vowel, then the number side is odd.
b) The letter side is a vowel if and only if the number side is even.

For the part (a) because there is only one case we cannot allow, T->F, you need to turn over only the vowels.

For the part (b), however, you need to turn over any vowel and any odd number.

What exactly did I prove? Wasn't the proof in the original statement already? Im a bit confused, care to elaborate please.

 

[pka]

To check the truth of the sentence “If the letter side is a vowel, then the number side is odd.” all one has to do is to check each vowel. If each has an odd number paired with it then the sentence is true. You see, even if some odd number is paired with a consonant that does change the truth of the sentence.