1.

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) 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.


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