Consider the following 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 The trophy was not awarded Arrange the steps in the correct order to show that these hypotheses imply the conclusion "It rained," using rules of interference.
Rank the options below.
1. We get the conclusion "it rained" from the given hypotheses.
2. Taking the contrapositive of (﹁rv → (SA ), we get(s^ ) →すrv ﹁ s and ( s v (r ^ imply that s v l, using addition.
3. The givenpremises are (﹁rv → (SA ) , s → t, and t
4. By modus ponens, ( s v (r^ ή and s v , imply r^ f and r^ fimplies r using simplification.
5. Let r be the proposition "t rains," let fbe the proposition "It is foggy," let s be the proposition "The sailing race will be held," let /b proposition "The lifesaving demonstration will go on," and let t be the proposition "The trophy will be awarded."
6. Applying De Morgan's law on ר(SA →ヤrv ﹁5, we obtain (าร ν רり→ (ГлかUsing and s → t, we get ﹁s is true