InterviewSolution
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InterviewSolution
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Write the component statements of the following compound statements and check whether the compound statement is true or false:(i) To enter into a public library children need an identification card from the school or a letter from the school authorities.(ii) All rational numbers are real and all real numbers are not complex.(iii) Square of an integer is positive or negative.(iv) x = 2 and x = 3 are the roots of the equation 3x2 – x – 10 = 0.(v) The sand heats up quickly in the sun and does not cool down fast at night. |
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Answer» (i) The components of the compound statement are: P: To get into a public library children need an identity card. Q: To get into a public library children need a letter from the school authorities. Both P and Q are true. Hence, the compound statement is true. (ii) The components of the compound statement are: P: All rational number is real. Q: All real numbers are not complex. P is true and Q is false then P and Q both are False. Hence, the compound statement is False (iii) The components of the compound statement are: P: Square of an integer is positive. Q: Square of an integer is negative. Both P and Q are true. Hence, the compound statement is True. (iv) The components of the compound statement are: P: x=2 is a root of the equation 3x2 – x – 10 = 0 Q: x = 3 is a root of the equation 3x2 – x – 10 = 0 P is true, but Q is false then P and Q both are False. Hence, the compound statement is False. (v) The components of the compound statement are: P: The sand heats up quickly in the sun. Q: The sand does not cool down fast at night. P is false and Q is also false then P and Q both are False. Hence, the compound statement is False. |
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