Question

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

A. n is not divisible by 6 or n is divisible by both 2 and 3.
B. n is not divisible by 6 and n is divisible by both 2 and 3.
C. n is divisible by 6 or 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. n is divisible by 6 and n is divisible by both 2 and 3.
F. n is not divisible by 6 or n is not divisible by both 2 and 3.
G. n is divisible by 6 or n is not divisible by both 2 and 3.
H. n is not divisible by 6 and n is not divisible by both 2 and 3.

Answer 1

H.''n is not divisible by 6 and n is not divisible by both 2 and 3.

Step-by-step explanation:

We are given that a statement ''n is divisible by 6 or n is divisible by both 2 and 3.''

We have to write the negation of the given statement.

Negation: If a statement p is true then its negations is p is false.

n is divisible by 6 then negation is n is not divisible by 6.

n is divided by both 2 and 3 then negation is n is not divisible by both 2 and 3.

Therefore, negation of given statement

''n is not divisible by 6 and n is not divisible by both 2 and 3.

Hence, option H is true.

Explanation:

Answer 2

H.''n is not divisible by 6 and n is not divisible by both 2 and 3.

Explanation:

We are given that a statement ''n is divisible by 6 or n is divisible by both 2 and 3.''

We have to write the negation of the given statement.

Negation: If a statement p is true then its negations is p is false.

n is divisible by 6 then negation is n is not divisible by 6.

n is divided by both 2 and 3 then negation is n is not divisible by both 2 and 3.

Therefore, negation of given statement

''n is not divisible by 6 and n is not divisible by both 2 and 3.

Hence, option H is true.