Answer to Question #121796 in Discrete Mathematics for wayne

Question

Which of the following pairs of statements are logically equivalent? I.
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'.

II.Statement 1: Joe tells you that he is an engineer and he studied in Mapua.
Statement 2: If Joe is lying, then Joe is not an engineer or he did not study in Mapua.

Answer 1

Statement 1: Joe tells you that he is an engineer and he studied in Mapua are logically equivalent to Statement 2: If Joe is lying, then Joe is not an engineer or he did not study in Mapua.

Because in the first case in statement 1 - " either I watched 'Crashlanding on You' or you watched 'Money Heist'" - it is condition "OR" but also "It is not true" - negation. In statement 2 "I did not watch 'Crashlanding on You' and you watched 'Money Heist'" equivalent to " either I watched 'Crashlanding on You' or you watched 'Money Heist'" but here it is not negation.