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.
(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.
We know if P and Q are true then P and Q must also be 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.
We know, P is true and Q is False then P and Q is 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.
We know that, if P and Q are true then P or Q is 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
Here, P is true, but Q is False then P and Q is 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.
Here, P is false and Q is also False then P and Q is False.
Hence, The compound statement is False.