Identify the quantifiers and write the negation of the following state

1.	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» (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”.

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»

(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”.