IGDTUW 2026 — Computer PYQ

The correct option is (b) $A$ AND $B$.

Detailed Solution & Explanation

In set theory and mathematical logic, operations on sets have a direct correspondence with logical connectives.

Definition of Intersection:

The intersection of two sets $A$ and $B$, denoted by $A\cap B$, is the set containing all elements that belong to both set $A$ and set $B$ simultaneously.

Mathematically, it is written in set-builder notation as:

$$A\cap B=\{x:x\in A\text{ and }x\in B\}$$

Comparison of Options:

• (a) $A$ OR $B$: This represents the Union of two sets ($A\cup B$). It includes elements that are in $A$, or in $B$, or in both.

• (b) $A$ AND $B$: This represents the Intersection ($A\cap B$). The word "AND" signifies that an element must satisfy both conditions to be included in the intersection.

• (c) $A$ XOR $B$: This represents the Symmetric Difference ($A\Delta B$). It includes elements that are in either $A$ or $B$, but not in both.

• (d) $A$ NOT $B$: This represents the Set Difference ($A\setminus B$ or $A-B$). It includes elements that belong to $A$ but do not belong to $B$.

Thus, the operation of intersection corresponds exactly to the logical conjunction AND.