Question

Negate each of the following statements: 

(i) All the students complete their homework. 

(ii) There exists a number which is equal to its square.

Answer 1

(i) Negation of statement p is "not p." The negation of p is symbolized by "~p." The truth value of ~p is the opposite of the truth value of p. 

The negation of the statement 

All the students complete their homework. 

is 

Some of the students did not complete their homework. 

(ii) The negation of the statement 

There exists a number which is equal to its square. is 

For every real number x, x²≠x.