Question

A Union B = A Intersection B, A=B

Answer 1

Yes ..if the elements of both groups are equal then it will be possible.
Eg:a={1,2,3},b={1,2,3}
Then 1)a union b
={123}u{123}
={123123}
A union b={123}
2)a intersection b
={123}n{123}
={123}
Hence proved