Form the biconditional statement p⟷q, where
(i) p: The unit digits of an integer is zero.
q: It is divisible by 5.
(ii) p: A natural number is odd.
q: Natural number is not divisible by 2.
(iii) p: A triangle is an equilateral triangle.
q: All three sides of a triangle are equal.

Prove the following statement by contradiction method.
p: The sum of an irrational number and a rational number is irrational.

Show that the following statement is true by the method of contrapositive.

p: If x is an integer and x² is even, then x is also even.

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 AP.

Translate the following statements into symbolic form.
(i) Rahul passed in Hindi and English.
(ii) x and y are even integers.
(iii) 2, 3 and 6 are factors of 12.
(iv) Either x or x + 1 is an odd integer.
(v) A number is either divisible by 2 or 3.
(vi) Either x = 2 or x = 3 is a root of 3x² – x – 10 = 0
(vii) Students can take Hindi or English as an optional paper.