NCERT Class XI Mathematics - Mathematical Reasoning - Solutions
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Question : 6
Total: 25
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 equation3 x 2
(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
Solution:
(i) The compound statement has the connecting word ‘and’.Component statements arep: All rational numbers are real.q: All real numbers are not complex.(ii) The compound statement has the connecting word ‘or’. Component statements are:
p: Square of an integer is positive.
q: Square of an integer is negative.
(iii) The compound statement has the connecting word ‘and’. Component statements are:
p: The sand heats up quickly in the sun.
q: The sand does not cool down fast at night.
(iv) The compound statement has the connecting word ‘and’. Component statements are:
p: x = 2 is a root of the equation3 x 2
q: x = 3 is a root of the equation3 x 2
p: Square of an integer is positive.
q: Square of an integer is negative.
(iii) The compound statement has the connecting word ‘and’. Component statements are:
p: The sand heats up quickly in the sun.
q: The sand does not cool down fast at night.
(iv) The compound statement has the connecting word ‘and’. Component statements are:
p: x = 2 is a root of the equation
q: x = 3 is a root of the equation
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