\[ \begin{array}{l} PQ + \overline{PQR} + \overline{PQRS} \\ = PQ + \overline{PQ}(R + RS) \\ = PQ + \overline{PQ} \left((R + R)(R + S)\right) \quad \text{(as we know } A + BC = (A + B)(A + C) \text{)} \\ = PQ + \overline{PQ} (R + S) \quad \text{(as we know } R + \overline{R} = 1 \text{)} \\ = Q(P + \overline{P}(R + S)) \quad \text{(Taking Q as common)} \\ = Q((P + \overline{P})(P + R + S)) \quad \text{(as we know } A + BC = (A + B)(A + C) \text{)} \\ = Q(P + R + S) \\ = PQ + QR + QS \\ = \text{Option A is correct} \end{array} \]