Question

if A union B is equal to A intersection B then proof A is equal to B​

Answer 1

let x∈A then x∈A∪B

since , A∪B=A∩B

x∈A∩B

So, x∈B

i.e., if an element belongs to set A, then it must belong to set B also.

∴A⊂B

Similarly, if y∈B then, y∈A∪B

Since A∪B=A∩B

y∈A∩B

So, y∈A

∴ if y∈B

then y∈A

A⊂A

from (i) and (ii)

A⊂B and B⊂A

thus A=B