**Question:**

**Write the negation of the following simple statements**

**(i) The number 17 is prime.**

**(ii) 2 + 7 = 6.**

**(iii) Violets are blue.**

**(iv) √5 is a rational number.**

**(v) 2 is not a prime number.**

**(vi) Every real number is an irrational number.**

**(vii) Cow has four legs.**

**(viii) A leap year has 366 days.**

**(ix) All similar triangles are congruent.**

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

**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.**

The negation of the statement is √5 is not a rational number.

**(v) 2 is not a prime number.**

The negation of the statement is “2 is a prime number”.

**(vi) Every real number is an irrational number.**

The negation of the statement is “Every real number is not an irrational number”.

**(vii) Cow has four legs.**

The negation of the statement is “Cow does not have four legs”.

**(viii) A leap year has 366 days.**

The negation of the statement is “A leap year does not have 366 days”.

**(ix) All similar triangles are congruent.**

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.**

The negation of the statement is Area of a circle is not same as the perimeter of the circle.

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