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