Question 4 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.
Class X1 - Maths -Mathematical Reasoning Page 345
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(i) if you watch television , then your mind is free and if your mind is fee , then you watch television.
=> you watch television if and only if your mind is free.
(ii) For you get an A grade , if it is necessary and sufficient that you do all the homework regularly.
=> You get Grade A if and only if you do all the home regularly.
(iii) if a quadrilateral is equiangular , then it's a rectangle and if a quadrilateral is a rectangle then it is equiangular.
=> A quadrilateral is equiangular if and only if it is a rectangle.
=> you watch television if and only if your mind is free.
(ii) For you get an A grade , if it is necessary and sufficient that you do all the homework regularly.
=> You get Grade A if and only if you do all the home regularly.
(iii) if a quadrilateral is equiangular , then it's a rectangle and if a quadrilateral is a rectangle then it is equiangular.
=> A quadrilateral is equiangular if and only if it is a rectangle.
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