Suppose n is even then n = 2m for some m.

therefore n = 2m

obviously n-1=2m - 1 is odd

Alternatively

if n- 1 is odd then (n-1) + 1 = is n which is even for n-1 is odd.

we can also say that for n-1 being odd implies em-1 is odd where n = 2m for some m.

thus (n-1) = (2m-1)-1 = 2m-2 = 2(m-1) which is even.

Hence the proof