Answer to Question #273595 in Discrete Mathematics for Blizzy

Question

The negation of the statement " 52 is divisible by 4 and 7" is

Answer 1

Let $p$ = "52 is divisible by 4" and $q$ = "52 is divisible by 7". Then $p\land q$ denotes the statement "52 is divisible by 4 and 7". The negation of $p\land q$ is equivalent by De Morgan's Law to $\neg p\lor \neg q,$ and hence the negation of the statement " 52 is divisible by 4 and 7" is

"52 is not divisible by 4 or 52 is not divisible by 7".