Assume that m and n are particular integers Is 6 m 8 n even

Assume that m and n are particular integers. Is 6 m + 8 n even? Why? (Can you apply the definition?) Assume that r and s are particular integers. Is 10rs + 7 odd? Why? (Can you apply the definition?)

Solution

1.

6m+8n=2*3m+2*4n=2(3m+4n)

Hence, 6m+8n is a multiple of 2.

Hence 6m+8n is even

2.

10rs=2*5rs.

Hence 10rs is even

7 is an odd number

Sum of an even number and odd number is an odd number.

Hence, 10rs+7 is odd.