If a rectangle is a square, then all its four sides are equal. q: If all the four sides of a rectangle are equal, then the rectangle is a square. p: If the sum of digits of a number is divisible by , then the number is divisible by . q: If a number is divisible by , then the sum of its digits is divisible by .
Solution (i) A rectangle is a square if and only if all its four sides are equal. A number is divisible by if and only if the sum of its digits is divisible by . EXERCISE . .
Rewrite the following statement with “if-then” in five different ways conveying the same meaning. If a natural number is odd, then its square is also odd. . Write the contrapositive and converse of the following statements.
If x is a prime number, then x is odd. If the two lines are parallel, then they do not intersect in the same plane. (iii) Something is cold implies that it has low temperature. (iv) You cannot comprehend geometry if you do not know how to reason deductively.
(v) x is an even number implies that x is divisible by . . Write each of the following statements in the form “if-then” You get a job implies that your credentials are good. The Bannana 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 an A + in the class, it is necessary that you do all the exercises of the book. MATHEMATICAL REASONING . Given statements in (a) and (b).
Identify the statements given below as contrapositive or converse of each other. (a) If you live in Delhi, then you have winter clothes. If you do not have winter clothes, then you do not live in Delhi. If you have winter clothes, then you live in Delhi.
(b) If a quadrilateral is a parallelogram, then its diagonals bisect each other. If the diagonals of a quadrilateral do not bisect