NIMCET 2026 — Mathematics PYQ

To solve this, we first recall the definition of the symmetric difference of two sets $A$ and $B$:

$$A\Delta B=(A\setminus B)\cup (B\setminus A)=(A\cap B^c)\cup (B\cap A^c)$$

Given the expression $(A\Delta B)\cap C$, we can distribute $\cap C$ into the definition:

$$(A\Delta B)\cap C=((A\cap B^c)\cup (B\cap A^c))\cap C$$

$$=((A\cap B^c)\cap C)\cup ((B\cap A^c)\cap C)$$

This matches option (c), confirming it is correct.