Question

If $p$ and $q$ are substatements "A natural number is odd" and "A natural number is not divisible by $2$" respectively, then the biconditional statement $p\iff q$ is

• A. If a natural number is odd, then it is not divisible by $2$.
• B. A natural number is odd, if and only if it is divisible by $2$.
• C. A natural number is odd, if and only if it is not divisible by $2$.
• D. If a natural number is odd, then it is divisible by $2$.

Answer 1

The correct option is C A natural number is odd, if and only if it is not divisible by $2$.

We know that , $p\iff q$ is represented as $p$ if and only if $q$

Given, $p:$ A natural number is odd
$q:$ A natural number is not divisible by $2$

$\therefore p\iff q:$ A natural number is odd, if and only if it is not divisible by $2.$