Use rules of inference to show that the hypotheses "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," "If the sailing race is held, then the trophy will be awarded," and "The trophy was not awarded" imply the conclusion "It rained."
I have this so far:
Let p, q, r, s, and t be the propositions.
p: It rained.
q: It is foggy.
r: The sailing race is held.
s: The lifesaving demonstration will go on.
t: The trophy is awarded.
Then the argument form is
( -p V -q) --> (r /\ s)
r --> t
How do I break the argument down? The first premise is the issue for me.