Given below are some pairs of statements. Combine each pair using if and only if:
(i) p: If a quadrilateral-is equiangular, then it is a rectangle.
q: If a quadrilateral is a rectangle, then it is equiangular.
(ii) p: If the sum of the digits of a number is divisible by 3, then the number is divisible by 3.
q: If a number is divisble by 3, then the sum of its digits is divisible by 3.
(iii) p: A quadrilateral is a parallelogram if its diagonals bisect each other.
q: If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
(iv) p: If f(a) = 0, then (x -a) is a factor of polynomial f(x).
q: If (x-a) is a factor of polynomial f(x), thenf(a) = 0.
(v) p: If a square matrix A is invertible, then |A| is nonzero.
q: If A is a square matrix such that |A| is nonzero, then A is invertible.

Explanation

(i) A quadrilateral is a rectangle if and only if it is equiangular.
(ii) A number is divisible by 3 if and only if the sum of its digits is divisible by 3.
(iii) A quadrilateral is a parallelogram if and only if its diagonals bisect each other.
(iv) (x - a) is a factor of polynomial f(x) if and only if f(a) = 0.
(v) A square matrix A is invertible if and only if |A| is nonzero.