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 divisible 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), then f(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.


(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 the digits of the number 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) Square matrix A is invertible if and only if |A| is nonzero.


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