Write each of the following statement in the form “if-then”.

(i) You get a job implies that your credentials are good.

(ii) The Banana trees will bloom if it stays warm for a month.

(iii) A quadrilateral is a parallelogram if its diagonals bisect each other.

(iv) To get A⁺ in the class, it is necessary that you do the exercises of the book.

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Solution

(i) If you get a job, then your credentials are good.

(ii) If the Banana tree stays warm for a month, then it will bloom.

(iii) If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

(iv) If you want to get an A⁺ in the class, then you do all the exercises of the book.

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Write each of the following statements in the form 'if ... then':

(i) A rhombus is a square only if each of its angles measures $90^{\circ} .$

(ii) When a number is a multiple of 9, it is necessarily a multiple of 3.

(iii) You get a job implies that you credentials are good.

(iv) Atmospheric humidity increases only if it rains.

(v) If a number is not a multiple of 3, then it is not a multiple of 6.

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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