If A and B be any two sets such that A Δ B = A, then A ∩ B is

The notation $\Delta$ 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:
$$A\Delta B=(A-B)\cup (B-A)$$
We are given the condition:
$$(A-B)\cup (B-A)=A$$
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:
$$B-A=\varphi ⟹B\subseteq A$$
If $B$ is a subset of $A$ ($B\subseteq A$), 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 $B\subseteq A$ and $A-B=A$ to be true simultaneously, set $B$ must be the empty set:
$$B=\varphi$$
Since $B$ is an empty set ($\varphi$), the intersection of $A$ with an empty set is also empty:
$$A\cap B=A\cap \varphi =\varphi$$