Prove If n is odd then n1 and n1 are both evenSolutiongiven

Prove: If n is odd, then n+1 and n-1 are both even.

given

n is a odd number

asked to prove n+1 and n-1 are even

Definition of even and odd numbers

Even numbers = 2n

Odd numbers = 2n+1 or 2n-1 (an even number +1 or -1 is an odd number)

now

Lets Find out if an odd number added with 1 is odd or even

take odd numbers in the place of n i.e.., 1,3,5,7.....n

now adding them with 1

1+1= 2

3+1 = 4

5 + 1=6

these all are even numbers so simillarly n+1 is also even

now

Lets Find out if an odd number subtracted with 1 is odd or even

take odd numbers in the place of n i.e.., 1,3,5,7.....n

now subtracting them with 1

1-1= 0

3-1 = 2

5 - 1=4

these all are even numbers so simillarly n-1 is also even