Question

# For each of the following compound statements first identify the connecting words and then break it into component statements. (i) All rational numbers are real and all real numbers are not complex. (ii) Square of an integer is positive or negative. (iii) The sand heats up quickly in the Sun and does not cool down fast at night. (iv) x = 2 and x = 3 are the roots of the equation 3 x 2 – x – 10 = 0.

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Solution

## A compound statement is made up of two or more statements and each statement in the compound statement is known as component statement. (i) The given compound statement is: All rational numbers are real and all real numbers are not complex. The connecting word in the given statements is “and”, so the statement can break into component statements which are as follows: A: All rational numbers are real. B: All real numbers are not complex. (ii) The given compound statement is: Square of an integer is positive or negative. The connecting word in the given statements is “or”, so the statement can break into component statements which are as follows: A: Square of an integer is positive. B: Square of an integer is negative. (iii) The given compound statement is: The sand heats up quickly in the sun and does not cool down fast at night. The connecting word in the given statements is “and”, so the statement can break into component statements which are as follows: A: The sand heats up quickly in the sun. B: The sand does not cool down fast at night. (iv) The given compound statement is: x=2 and x=3 are the roots of the equation 3 x 2 −x−10=0 . The connecting word in the given statements is “and”, so the statement can break into component statements which are as follows: A: x=2 is the root of the equation 3 x 2 −x−10=0 . B: x=3 is the root of the equation 3 x 2 −x−10=0 .

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