Answer to Question #131779 in Math for Surada

Question

Which of the following pairs of statements are logically equivalent?

I. Statement 1: It is not true that either I watched 'Avengers' or you watched 'Justice League'.

Statement 2: I did not watch 'Avengers' and you watched 'Justice League'.

II. Statement 1: George tells you that he is an engineer and he studied in MIT.

Statement 2: If George is lying, then George is not an engineer or he did not study in MIT.

A. I only

B I and II

C. II only

D. Neither I nor II

Answer 1

Statements 1 and 2 from II are logically equivalent because they explain the same situation but using opposite explanation, so if George is telling truth, then he is an engineer and he studied in MIT, but if he is lying, then he is not an engineer and he didn't study in MIT.

But statements 1 and 2 from I are not logically equivalent because statement 1 tells us that it is true if we both either saw the two films or not. But statement 2 provides the situation, when only one of us saw the film.

So, the correct answer is C II only.