Step 1: Write out the symmetric difference. By definition $A\Delta B=(A\cap B^c)\cup(B\cap A^c)$, the elements in exactly one of $A$ or $B$. We must find which option is NOT equal to $(A\Delta B)\cap C$. Step 2: Intersect with $C$. $(A\Delta B)\cap C=((A\cap B^c)\cap C)\cup((B\cap A^c)\cap C)$. This is precisely option (C), so (C) is equal. Step 3: Check option (A). $(A\cap C)\Delta(B\cap C)$ keeps the elements of $C$ that lie in exactly one of $A,B$, which is the same set. So (A) is equal. Step 4: Check option (B). $(A\cup B)\cap C$ with the part $A\cap B\cap C$ removed keeps elements of $C$ in $A$ or $B$ but not in both, again the symmetric-difference part inside $C$. So (B) is equal. Step 5: Examine option (D). $(A\cap B)^c\cap C$ contains every element of $C$ that is merely not in both $A$ and $B$, which includes elements in neither $A$ nor $B$. The symmetric difference excludes those. So (D) is strictly larger. Step 6: Conclude. Option (D) is the one that is not the same as $(A\Delta B)\cap C$. \[ \boxed{(A\cap B)^c\cap C} \]