If A and B are any two sets such that AΔB=A, then A∩B is equal to

The notation Δ represents the symmetric difference between two sets, which is defined as the union of elements that belong to either of the sets but not to their intersection:
AΔB=(A−B)∪(B−A)
We are given the condition:

(A−B)∪(B−A)=A
Let's look at the components of this union:

For the union to equal exactly set A, the second component (B−A) cannot contain any elements that lie outside of A. This means (B−A) must be an empty set:

B−A=ϕ⟹B⊆A
If B is a subset of A (B⊆A), then the first component (A−B) simplifies to just A excluding elements of B.

Substituting this back, the symmetric difference becomes A−B=A, which means no elements of B are in A. For both B⊆A and A−B=A to be true simultaneously, set B must be the empty set:

B=ϕ
Since B is an empty set (ϕ), the intersection of A with an empty set is also empty:

A∩B=A∩ϕ=ϕ