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.
(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.”
(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.”
