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 3x2−x−10=0

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Solution

(i) Here the connecting word is 'and'The component statements are as followsp: All rational numbers are realq: All real numbers are not complex(ii) Here the connecting word is 'or'The component statements are as followsp: Square of an integer is positiveq: Square of an integer is negative (iii) Here the connecting word is 'and'The component statements are as followsp: The sand heats up quickly in the sunq: The sand does not cool down fast at night(iv) Here the connecting word is 'and'The component statements are as followsp:x=2 is a root of the equation 3x2−x−10=0q:x=3 is a root of the equation 3x2−x−10=0

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