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Rewrite the following statement in the form `p` if only if`q :` `q :` if a quadrilateral is equiangular, then it is a rectangle and if a quadrilateral is a rectangle, then it is equiangular.

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A quadrilateral is equiangular if and only if it is a rectangle
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Rewrite the following statements in the form: 'p if and only if q' p: A quadrilateral is equiangular. q: A quadrilateral is a rectangle.

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.

Rewrite each of the following statements in the form “p if and only if q" (i) p: If you watch television, then your mind is free and if your mind is free, then you watch television. (ii) q: For you to get an A grade, it is necessary and sufficient that you do all the homework regularly. (iii) r : If a quadrilateral is equiangular, then it is a rectangle and if a quadrilateral is a rectangle, then it is equiangular.

Prove that, any rectangle is a cyclic quadrilateral.

Prove that, any rectangle is a cyclic quadrilateral.

Explain why a rectangle is a convex quadrilateral.

The following statement (p to q) to [(~p to q) to q] is

Write the following statement in five different ways, conveying the same meaning : p : If a triangle is equiangular, then it is an obtus-angled triangle.

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