On integers, (aRb) holds when (a\equiv b \pmod{3}), and (aSb) holds when (a\equiv b \pmod{5}). In (R\cap S), which is the equivalence class of (7)?

Correct answer: ({x\in\mathbb{Z}:x\equiv 7 \pmod{15}})

Step 1: In (R\cap S), numbers must have the same remainder modulo (3) and modulo (5). Step 2: Since (3) and (5) are coprime, this is the same as congruence modulo (15). Step 3: Hence the class of (7) is the integers congruent to (7) modulo (15).