Question

Write the following statement in symbolic form and find its truth value:
$\forall nϵN,n^2+n$ is an even number and $n^2-n$ is an odd number

Answer 1

$\forall n\in N$

$p:n^2+n$ is a even number

$q:n^2-n$ is an odd number.

Then, $n^2+n$ is a even number and $n^2-n$ is an odd number.

It can also be written as:

$p\wedge q$

Now,

$n^2+n=n(n+1)$, product of two continuous natural numbers is always even, Hence, $p$ is True.

$n^2-n=n(n-1)$, product of two continuous natural numbers is always even, Hence, $q$ is False.

Hence, $p\wedge q$ is False.