Answer to Question #272535 in Discrete Mathematics for Hana

Question

Which of the following pairs of statements are logically equivalent?

   I.   Statement 1: It is not true that both you have pneumonia and I got flu.

       Statement 2: Either you have no pneumonia or I have no flu.

   II.   Statement 1: It is not true that either I watched 'Crashlanding on You' or you watched 'Money Heist'.

       Statement 2: I did not watch 'Crashlanding on You' and you watched 'Money Heist'.

a) II only

b) I only

c) I and II

d) Neither I nor II

Answer 1

I.

 Statement 1 is equivalent to: you have not pneumonia and I got flu, or you have pneumonia and I got not flu, or you have not pneumonia and I got not flu

Statement 2 is equivalent to: you have not pneumonia and I got flu, or you have pneumonia and I got not flu

So, Statement 1 is not equivalent to Statement 2

II.

 Statement 1 is equivalent to: I watched 'Crashlanding on You' and you did not watch 'Money Heist', or I did not watch 'Crashlanding on You' and you watched 'Money Heist'

So, Statement 1 is not equivalent to Statement 2

Answer: d) Neither I nor II