Prove that if n is a positive integer, then n is even if and only if 7n + 4 is even.

Solution:

Let f(n) = 7n + 4

Consider few samples of n(positive integer)

n = 2, 4, 6, 8,10

If n = 2 then 7(2) + 4= 14 + 4 = 18 (even)

If n = 4 then 7(4) + 4 = 28 + 4 = 32 (even)

If n = 6 then 7(6) + 4 = 42 + 4 = 46 (even)

If n = 8 then 7(8) + 4 = 56 + 4 = 60 (even)

If n = 10 then 7(10) + 4 = 70 + 4 = 74 (even)

Therefore, we can prove that if n is even, then 7n + 4 is also even.

Prove that if n is a positive integer, then n is even if and only if 7n + 4 is even.

Summary:

Thus when n is a positive integer, if n is even then 7n + 4 is also even.