Question

Choose the reasoning used
David plays video games if and only if he finishes his homework
David did not play video games on Wednesday
therefore David did not finish his homework on Wednesday
Choices: inductive deductive invaild

Answer 1

Invalid, methinks.

http://en.wikipedia.org/wiki/Denying_the_antecedent

Answer 2

i would say "valid" because "if and only if" means just that. if he doesn't finish his homework he doesn't play,and if he finishes he does play

Answer 3

It's a misleading real-world example example for "if and only if".

The statement says if he finished his homework, he HAS TO play video-games, and
if he didn't finish his homework, he CANNOT play video-games.

I would choose something like:
I will go to the park if and only if it doesn't rain.
This means:
If it doesn't rain, I WILL go to the park.
If it rains, I WILL NOT go to the park.

Answer 4

In that case sorry for giving the wrong answer.
http://en.wikipedia.org/wiki/If_and_only_if

The above article basically says 'if and only if' means equivalency so it returns true if both are false or both are true.
A - David plays video games
B - David finishes his homework

A B true
A ¬B false
¬A B false
¬A ¬B true

The sentece is therefore true if David does his homework and plays video games or if David doesn't do his homework and doesn't play video games. This should be deductive reasoning.