Let A n element of Z n 8a 7 for some integer a B m eleme

Let A = {n element of Z| n = 8a - 7 for some integer a} B = {m elementof Z| m = 4(2b + 1) -3 for some integer b} Is A = B? Explain.

Solution

We are given

A={ n E Z| n=8a-7 for some integer a}

B={ m E Z| m=4(2b+1)-3 for some integer b}

m=4(2b+1)-3

m=8b+4-3

m=8b+1

Since, b is a integer

so, we can replace b as b-1

m=8(b-1) +1

m=8b-8+1

m=8b-7

so, we will get

B={ m E Z| m=8b-7 for some integer b}

so, we can see that

A={ n E Z| n=8a-7 for some integer a}

B={ m E Z| m=8b-7 for some integer b}

Hence ,

A=B .............Answer