Form the biconditional statement p ↔ q, where

p : A triangle is an equilateral triangle.

q : All three sides of a triangle are equal.

Form the biconditional statement p ↔ q, where

p : The unit digit of an integer is zero.

q : It is divisible by 5.

Form the biconditional statement p ↔ q, where

p : A natural number n is odd.

q : Natural number n is not divisible by 2.

Write down the contrapositive of the following statements:

(i) If x = y and y = 3, then x = 3.

(ii) If n is a natural number, then n is an integer.

(iii) If all three sides of a triangle are equal, then the triangle is equilateral.

(iv) If x and y are negative integers, then xy is positive.

(v) If natural number n is divisible by 6, then n is divisible by 2 and 3.

(vi) If it snows, then the weather will be cold.

(vii) If x is a real number such that 0 < x < 1, then x² < 1.

Write down the converse of following statements :

(i) If a rectangle ‘R’ is a square, then R is a rhombus.

(ii) If today is Monday, then tomorrow is Tuesday.

(iii) If you go to Agra, then you must visit Taj Mahal.

(iv) If the sum of squares of two sides of a triangle is equal to the square of third side of a triangle, then the triangle is right angled.

(v) If all three angles of a triangle are equal, then the triangle is equilateral.

(vi) If x : y = 3 : 2, then 2x = 3y.

(vii) If S is a cyclic quadrilateral, then the opposite angles of S are supplementary.

(viii) If x is zero, then x is neither positive nor negative.

(ix) If two triangles are similar, then the ratio of their corresponding sides are equal.