Prove 4k 5 k Z 4k 1 k ZSolutionWe are given to prove that

Solution

We are given to prove that

{4k+5: k E Z } = {4k+1: k E Z }

{4k+1: k E Z }

we know that k is an integer

so, k+1 will also be integer

so, we can replace k as k+1

we get

{4(k+1)+1: k E Z }

{4k+4+1: k E Z }={4k+5: k E Z }

so, we will get

{4k+5: k E Z } = {4k+1: k E Z }.................Answer