Find out which of the following sentences are statements and which are not. Justify your answer.

All triangles have three sides.

Rewrite the following statement in five different ways conveying the same meaning.

If a given number is a multiple of 6, then it is a multiple of 3.

State whether the following sentences are statements or not :

(i) The angles opposite to equal sides of a triangle are equal.

(ii) The moon is a satellite of earth.

(iii) May God bless you!

(vi) Asia is a continent.

(v) How are you?

Prove by direct method that for any integer ‘n’, n³ – n is always even.

The contrapositive of the statement

“If p, then q”, is

The negation of the statement

“Rajesh or Rajni lived in Bangalore” is

The negation of the statement

“72 is divisible by 2 and 3” is

Identify the Quantifiers in the following statements.

(i) There exists a triangle which is not equilateral.

(ii) For all real numbers x and y, xy = yx.

(iii) There exists a real number which is not a rational number.

(iv) For every natural number x, x + 1 is also a natural number.

(v) For all real numbers x with x > 3, x2 is greater than 9.

(vi) There exists a triangle which is not an isosceles triangle

(vii) For all negative integers x, x³ is also a negative integers.

(viii) There exists a statement in above statements which is not true.

(ix) There exists a even prime number other than 2.

(x) There exists a real number x such that x² + 1 = 0.

The negation of the statement “The product of 3 and 4 is 9” is

The statement

“If x² is not even, then x is not even” is converse of the statement

The contrapositive of the statement

“If 7 is greater than 5, then 8 is greater than 6” is