Question

Identify the quantifiers and write the negation of the following statements.

(i) For all even integers x, x² is also even.

(ii) There exists a number which is a multiple of 6 and 9.

Answer 1

(i) For all even integers x, x² is also even.

The quantifier is “For All”.

The negation of the statement is-

“There exists an even integer x such that x² is not even”.

(ii) There exists a number which is a multiple of 6 and 9.

The quantifier is “There exists”.

The negation of the statement is-

“There does not exist a number which is a multiple of both 6 and 9”.