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.

Question

Philoid · Accepted Answer

(i) The component statements are:-

p: Number 3 is prime.

q: It is odd.

The connecting word is 'Or'

We know that number 3 is prime

Hence p is true

We know that number 3 is odd

Hence q is true.

(ii) The component statements are:-

p: All integers are positive.

q: All integers are negative.

The connecting word is 'Or'

Since all integers are not positive

Hence p is false

Since all integers are not negative

Hence q is false.

(iii) The component statements are:-

p: 100 is divisible by 3.

q: 100 is divisible by 11.

r: 100 is divisible by 5.

The connecting word is 'and'

Since, p is false, because 100 is not divisible by 3

q is false, because 100 is not divisible by 11

r is true, because 100 is divisible by 5

Hence p & q are false & r is true.

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.