Question

Find the component statements of the following compound statements and check whether they are true or false.

(i) Number 3 is prime or it is odd.

(ii) All integers are positive or negative.

(iii) 100 is divisible by 3, 11 and 5.

Answer 1

(i) The component statements are as follows.

p: Number 3 is prime.

q: Number 3 is odd.

Both the statements are true.

(ii) The component statements are as follows.

p: All integers are positive.

q: All integers are negative.

Both the statements are false.

(iii) The component statements are as follows.

p: 100 is divisible by 3.

q: 100 is divisible by 11.

r: 100 is divisible by 5.

Here, the statements, p and q, are false and statement r is true.