Discrete Structures Prove For all n element of N m element o

Discrete Structures

Prove. For all n element of N, (m element of even) ((n^2+3n) element of even)

Solution

since n is a even natural number

we know that the square of any even number is even, and multiplication of any number by an even number is also a even number.

that is n² is even for all n (natural even numbers).

and 3n is also even for all n (natural even numbers).

since the sum of two even numbers is also even

hence n² + 3n is even.