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Write the negation of the following simple statements
i) The number 17 is prime.

ii) 2 + 7 = 6.

iii) Violets are blue.

iv) $\sqrt{5}$ 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.

Answers (1)

i) Concept

We know that negation of p is “not p”, viz. symbolized as –p, also its truth value of –p is the opposite of the truth value of p. Thus, the negation of this statement will be – “The number 17 is not prime.”

ii) Concept

We know that negation of p is “not p”, viz. symbolized as –p, also its truth value of –p is the opposite of the truth value of p. Thus, the negation of this statement will be – $2+7\neq 6$

iii) Concept

We know that negation of p is “not p”, viz. symbolized as –p, also its truth value of –p is the opposite of the truth value of p. Thus, the negation of this statement will be –

“Violets are not blue”

iv) Concept

We know that negation of p is “not p”, viz. symbolized as –p, also its truth value of –p is the opposite of the truth value of p. Thus, the negation of this statement will be –

“ $\sqrt{5}$ is not a rational number."

v) Concept

We know that negation of p is “not p”, viz. symbolized as –p, also its truth value of –p is the opposite of the truth value of p. Thus, the negation of this statement will be –

“2 is a prime number.”

vi) Concept

We know that negation of p is “not p”, viz. symbolized as –p, also its truth value of –p is the opposite of the truth value of p. Thus, the negation of this statement will be –

“Every real number is not an irrational number.”

vii) Concept

We know that negation of p is “not p”, viz. symbolized as –p, also its truth value of –p is the opposite of the truth value of p. Thus, the negation of this statement will be –

“Cow does not have four legs.”

viii) Concept

We know that negation of p is “not p”, viz. symbolized as –p, also its truth value of –p is the opposite of the truth value of p. Thus, the negation of this statement will be –

“A leap year does not have 366 days.”

ix) Concept

We know that negation of p is “not p”, viz. symbolized as –p, also its truth value of –p is the opposite of the truth value of p. Thus, the negation of this statement will be –

“All similar triangles are not congruent.”

x) Concept

We know that negation of p is “not p”, viz. symbolized as –p, also its truth value of –p is the opposite of the truth value of p.

Thus, the negation of this statement will be – “Area of a circle is not same as the perimeter of the circle.”

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