Check the validity of the following statement.
(i) $p$: 125 is divisible by 5 and 7.
(ii) $q$: 131 is a multiple of 3 or 11.
Check the validity of the following statement.
(i) $p$: 125 is divisible by 5 and 7.
(ii) $q$: 131 is a multiple of 3 or 11.

Solution:

(i) $p$: 125 is divisible by 5 and 7

Let’s say, $q$: 125 is divisible by 5.

$r$: 125 is divisible 7.

So here, $q$ is true and $r$ is false.

Hence, $q\wedge r$ is False

As a result, $p$ is not valid.

(ii) Provided $q$ : 131 is a multiple of 3 or 11

Let’s say, $P$: 131 is a multiple of 3.

$Q$: 131 is a multiple of 11.

So here, $P$ is false and $Q$ is False

Hence, $P\vee Q$ is False

As a result, $q$ is not valid