Question

show that any positive odd integer is either even or odd.

Answer 1

the correct answer is odd

Answer 2

Hey!!!!!

let a be any positive integer.

let b = 2

Then by Euclid's Division Lemma,

=> a = 2q + r where 0 <= r < b

Thus r = 0 or 1

Case 1 , r = 0

=> a = 2q (even)

Case 2 , r = 1

=> a = 2q + 1 (odd)

HENCE PROVED