Question

What is the negation of the following: "If n is divisible by 6 then n is divisible by both 2 and 3."

A. n is divisible by 6 or n is divisible by both 2 and 3.
B. If n is divisible by both 2 and 3 then n is divisible by 6.
C. If n is divisible by 6 then n is divisible by both 2 and 3.
D. n is divisible by 6 and n is not divisible by both 2 and 3.
E. If n is not divisible by 6 then n is not divisible by both 2 and 3.
F. n is not divisible by 6 or n is divisible by both 2 and 3.
G. n is divisible by 6 and n is divisible by both 2 and 3.
H. n is not divisible by 6 and n is divisible by both 2 and 3.
I. If n is not divisible by 6 then n is divisible by both 2 and 3.
J. If n is not divisible by both 2 and 3 then n is not divisible by 6.
K. n is divisible by 6 or n is not divisible by both 2 and 3.

Answer 1

hippioo

Explanation:

hippi hipppokmkmkouse

Answer 2

D. n is divisible by 6 and n is NOT divisible by both 2 and 3.

Explanation:

The statement we want to negate is:

"IF n is divisible by 6 THEN n is divisible by both 2 and 3"

you should think of it as having one single antecedent (the sentence that follows after the IF) and one single consequent (the sentence that follows after THEN), as:

"IF ( n is divisible by 6 )THEN ( n is divisible by both 2 and 3 )"

This kind of statements are negated by saying that the antecedent is true, but the consequent isn't true (which is kind of saying that the antecedent being true doesn't necessarily make the consequent also true).

So the negation of the original statement is just:

"(n is divisible by 6) and NOT (n is divisible by both 2 and 3)"

which in common english is just

"n is divisible by 6 and n is NOT divisible by both 2 and 3."