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

Solution:

The components of a statement are its parts and are obtained by breaking it at the conjunctions.

(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

NCERT Solutions Class 11 Maths Chapter 14 Exercise 14.2 Question 3

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

Summary:

(i) p: Number 3 is prime, q: Number 3 is odd. Both the statements are true
(ii) p: All integers are positive, q: All integers are negative. Both the statements are false
(iii) 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