$($a$)$ Using truth table method, show that the hypotheses "There is no cricket match or there is traffic jam" and "There is cricket match or there is rain" imply the conclusion "There is traffic jam or there is rain."

$($b$)$ Using symbols and theory of inference, show that the hypotheses $"$If I did not go out, then it either rained or snowed" and "Neither it snowed nor I went out" imply the conclusion $"$It rained."