Truth Value Of Statement!

Number Theory Level 2

Find the truth value of the statement:

For all $n$ is belong to $\mathbb N$ , $n^2+n$ is an even number while $n^2-n$ is an odd number is $\text{\_\_\_\_\_\_\_\_\_\_}$ .

Notation : $\mathbb N$ denotes the set of natural numbers .

True False Both true and false Cannot be determined

1 solution

A Former Brilliant Member
Sep 1, 2016

To find whether the statement is true or false for all value which belong to Natural number. we need to solve for some values... as $n²+n$ for all value it should be even for all Natural numbers. ex.put the number $n={1,2,3... n}$ will gives the even number.

Now, $n²-n$ for all value it should be odd for all Natural numbers. ex.put the numbers $n={1,2,3...n}$ will gives the even numbers ... but mention that it must be odd number for all value of natural number. Then statement first is correct for all values but the second is incorrect for all values. so the statement will be false ...

Truth Value Of Statement!

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