On integers, (aRb) holds when (a\equiv b \pmod{4}), and (aSb) holds when (a\equiv b \pmod{6}). In (R\cap S), what is the equivalence class of (14)?

Correct answer: ({x\in\mathbb{Z}:x\equiv 2 \pmod{12}})

Step 1: In the intersection, the difference must be divisible by both (4) and (6). Step 2: This is congruence modulo (12). Step 3: (14) has remainder (2) modulo (12), so the class is (x\equiv 2 \pmod{12}).