Question

Write the negation of each of the following statements: 

(i) For every x ∈ N, x + 3 > 10 

(ii) There exists x ∈ N, x + 3 = 10

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 

For every x ∈ N, x + 3 > 10 

is 

There exist x ∈ N, such that x + 3 ≥ 10. 

(ii) 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 

For every x ∈ N, x + 3 = 10 

is 

There exist x ∈ N, such that x + 3 ≠ 10.