Question

prove that out of any two consecutive positive integers one and only one in even is even​

Answer 1

Let two consecutive positive integers are n and n + 1.

on dividing n by 2, let q be the quotient and r be the remainder .

using Euclid division Lemma :

n = 2q + r where 0< or =r <2.

therefore r=1,2

CASE 1. when r=0

n = 2q (even)

n+1 =2q +1 (odd)

CASE 2. when r =1

n =2q +1 (odd)

n+1 =2q+1+1

=2q+2

=2(q+1) ( even)

Hence out of any two consecutive positive integers one and only one is even.

Hope the answer helps you.

Answer 2

Refer to the attachment for the solution :)

Thnx✌️♥️~