Question

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 : If a quadrilateral is equiangular, then it is a rectangle and if a quadrilateral is a rectangle, then it is equiangular.
(iii) r : For you to get an A grade, it is necessary and sufficient that you do all the homework regularly.
(iv) s : If a tumbler is half empty, then it is half full and if a tumbler is half full, then it is half empty.

Answer 1

(i) You watch television if and only if your mind is free.

(ii) A quadrilateral is a rectangle if and only if it is equiangular.

(iii) You get an A grade if and only if you do all the homework regularly.

(iv) The tumbler is half empty if and only if the tumbler is half full.