GATE CS 1996 Q1.1 — Sets, Relations and Functions

We are given the expression:
$S = (A - B) \cup (B - A) \cup (A \cap B)$

We can analyze this by understanding what each term represents in a Venn diagram:

• $(A - B)$ represents the elements belonging exclusively to $A$ (i.e., in $A$ but not in $B$).
• $(B - A)$ represents the elements belonging exclusively to $B$ (i.e., in $B$ but not in $A$).
• $(A \cap B)$ represents the elements belonging to both $A$ and $B$.

Taking the union of these three mutually disjoint regions covers all elements that belong to $A$, $B$, or both. Therefore:

Thus, the correct option is A.