2) Given the hypotheses:

i) If it does not rain or if it is not foggy, then the sailing race will be held and the lifesaving demonstration will go on.

ii) If the sailing race is held, then the trophy will be awarded.

iii) The trophy was not awarded.

Prove the conclusion: It rained.

by translating all statements into corresponding symbolic statements using letters, then use rules of inference to deduce the conclusion from the hypotheses. STATE the rule of inference you use at each step. The table of rules of inference is given below.