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Question -

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.



Answer -

(i) Thecomponents 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 theschool authorities.

Both P and Q are true.

Hence, the compound statement is true.

(ii) Thecomponents 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) Thecomponents 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) Thecomponents of the compound statement are:

P: x=2 is a root of the equation 3x– x – 10 =0

Q: x = 3 is a root of the equation 3x– x – 10= 0

P is true, but Q is false then P and Q both are False.

Hence, the compound statement is False.

(v) Thecomponents 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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