Using the 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...

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Extracted text: Using the 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." Fill in the blank: Step Reason 1. -t Hypothesis 2. s→t Hypothesis 3. -s Modus tollens using (1) and (2) 4. (¬r v¬f) → (s l) Hypothesis 5. (-(s A 1)) →¬(¬r v¬f) Contrapositive of (4) 6. (-sv¬I) → (r A f) De Morgan's law and double negative 7. -sv-| ? _, using (3) 8. raf Modus ponens using (6) and (7) 9. r Simplification using (8) O Resolution O Addition O Simplification O Disjunctive syllogism