How can you draw that conclusion from a single premise when there are other premises indicating that the movie was indeed seen. This makes no sense. Also, you did the contrapositive incorrectly in the reduction.

The correct answer choice says that IF Billy did not eat his hat, then a Fat Guy/Beautiful Girl movie was NOT seen.

As you know, this follows from the contrapositive of the bi-conditional.

Your question is "how can you conclude this if you know that he DID see a Fat Guy/Pretty Girl movie". The answer is that whether he did or did not see the movie, and whether he did or did not eat his hat, is not covered by the correct answer choice. The correct answer choice simply makes a statement about what would happen IF he had not seen the FG/BG movie.


If this seems strange, consider this simple example:

Premise 1: If that wooden object is a baseball bat, then it's a piece of sporting equipment.

Premise 2: It is a baseball bat.


What can be concluded here?

First, based on the two premises put together, you can conclude that the object is a piece of sporting equipment.

Second, you can also conclude, by the contrapositive of Premise 1, that IF the wooden object were NOT sporting equipment, it would not be a baseball bat.

But he said that he would eat the hat if and only if he saw the fg/bg on TV...

That does not stop him from seeing such movies in the theater. That would make the solution incorrect, right? If he hasn't eaten his hat, he could have still seen a FG/BG movie...

Adam,

You are correct.
The way this question is currently worded, it would be possible for Billy to see a FG/BG movie in the theater and not eat his hat.

We will change the wording to "Sure enough, this afternoon I saw some Seth Rogen movie ON TV where..."

Thanks,
Arcadia