Write the negation of the following simple statements

Solution:

(i) The number 17 is prime.

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 is “The number 17 is not prime”.

(ii) 2 + 7 = 6.

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 is “2 + 7 ≠ 6”.

(iii) Violets are blue.

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 is “Violets are not blue”.

(iv) √5 is a rational number.

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 is √5 is not a rational number.

(v) 2 is not a prime number.

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 is “2 is a prime number”.

(vi) Every real number is an irrational number.

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 is “Every real number is not an irrational number”.

(vii) Cow has four legs.

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 is “Cow does not have four legs”.

(viii) A leap year has 366 days.

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 is “A leap year does not have 366 days”.

(ix) All similar triangles are congruent.

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 is “All similar triangles are not congruent”.

(x) Area of a circle is same as the perimeter of the circle.

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 is Area of a circle is not same as the perimeter of the circle.