Question

Prove that every natural number is either even or odd. Hint: Use induction.

Answer 1

Note: natural numbers start at 1

Answer 2

1 is odd.
If k is even or odd then k+1 is even in the case k were odd or k+1 is odd if k were even.

Answer 3

ur base case looks fine, rest is messy still

Answer 4

1is odd
assume k is odd, then k=2s+1
so k+1=2s+1+1=2s+2=2(s+1) which is even

Answer 5

s is integer

Answer 6

thats right u need to prove the other case also where k can be even

Answer 7

right we can do that similarly

Answer 8

so k = 2s, and k + 1 = 2s + 1 which is odd