Answer
See the step by step work
Work Step by Step
We will show that these two sets are equal by showing that each is a subset of the other. Suppose x ϵ A Ո (AU B). Then x ϵ A and x ϵ (A U B) by the definition of intersection. Since (x ϵ A), we have proved that
the left-hand side is a subset of the right-hand side.
Conversely, let (x ϵ A). Then by the definition of union, x ϵ (A U B) as well. Since both of these are true, x ϵ A Ո (AU B) by the definition of intersection, and we have shown that the right-hand side is a subset of the left-hand side.
