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