Form the biconditional statement p ↔ q, where

p : The unit digit of an integer is zero.

q : It is divisible by 5.

Write down the negation of following compound statements

(i) All rational numbers are real and complex.

(ii) All real numbers are rationals or irrationals.

(iii) x = 2 and x = 3 are roots of the Quadratic equation x² – 5x + 6 = 0.

(iv) A triangle has either 3-sides or 4-sides.

(v) 35 is a prime number or a composite number.

(vi) All prime integers are either even or odd.

(vii) |x| is equal to either x or – x.

(viii) 6 is divisible by 2 and 3.

Rewrite each of the following statements in the form of conditional statements

(i) The square of an odd number is odd.

(ii) You will get a sweet dish after the dinner.

(iii) You will fail, if you will not study.

(iv) The unit digit of an integer is 0 or 5 if it is divisible by 5.

(v) The square of a prime number is not prime.

(vi) 2b = a + c, if a, b and c are in A.P.

Form the biconditional statement p ↔ q, where

p : A natural number n is odd.

q : Natural number n is not divisible by 2.

Form the biconditional statement p ↔ q, where

p : A triangle is an equilateral triangle.

q : All three sides of a triangle are equal.