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Question

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) The given statement is: *p*: “If you watch television, then your mind is free and if your mind is free, then you watch television.” The given statement can be written as follows:

“You watch television if and only if your mind is free.”

(ii) The given statement is: *q*: “For you to get an A grade, it is necessary and sufficient that you do all the homework regularly.” The given statement can be written as follows:

“You get an A grade if and only if you do all the homework regularly.”

(iii) The given statement is: *r*: “If a quadrilateral is equiangular, then it is a rectangle and if a quadrilateral is a rectangle, then it is equiangular.” The given statement can be written as follows:

“A quadrilateral is equiangular if and only if it is a rectangle.”

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