Re write 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.

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Solution

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

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

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

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Similar questions

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.

Rewrite each of the following statement 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 you 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 you regularly.

(iv) s : If atumbler is half empty, then it is half full and if a tumbler is half full, then it is ha;f empty.

Write each of the following using if and only if.

(i) In order to get A grade, it is necessary and sufficient that you do all the homework regularly.

(ii) If you watch television then your mind is free and if your mind is free then you watch television.

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