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Rewrite each of the following statements...

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.

Text Solution

AI Generated Solution

To rewrite the given statements in the form “p if and only if q,” we will analyze each statement carefully and identify the logical relationships involved. ### Step-by-Step Solution: 1. **Statement (i):** - Original: "If you watch television, then your mind is free and if your mind is free, then you watch television." - Analysis: This statement indicates a two-way relationship between watching television and having a free mind. It means that watching television implies a free mind, and having a free mind implies watching television. - Rewritten: "You watch television if and only if your mind is free." ...
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