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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: 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.
Answer:

Given statements are: 

(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.

Now these statements can be written in "if p then q form" as:

1. You watch a television if and only if your mind is free.

2. You will get grade A if and only if you do all the homework properly.

3. A quadrilateral is equiangular if and only if it is a rectangle.

 

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