Question

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. -s and (sv)→(r∧f) imply that -sv- using addition. Taking the contrapositive of (r∨f)→(s∧l), we get (s∧l)→¬(r∨f). The given premises are (¬r∨¬f)→(s∧l), s→t, and ¬t. Let r be the proposition "It rains," let f be the proposition "It is foggy," let s be the proposition "The sailing race will be held," let l be the proposition "The lifesaving demonstration will go on." and let t be the proposition "The trophy will be awarded." Applying De Morgan's law on ¬(s∧l)→¬(r∨f), we obtain (¬s∨¬l)→(¬r∧¬f). Using ¬t and s→t, we get ¬s is true. We get the conclusion "It rained" from the given hypotheses. By modus ponens, (¬s∨¬l)→(¬r∧¬f) and ¬s∨¬l imply ¬r∧¬f and ¬r∧¬f implies ¬r using simplification.

          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.
-s and (sv)→(r∧f) imply that -sv- using addition.
Taking the contrapositive of (r∨f)→(s∧l), we get (s∧l)→¬(r∨f).
The given premises are (¬r∨¬f)→(s∧l), s→t, and ¬t.
Let r be the proposition "It rains," let f be the proposition "It is foggy," let s be the proposition "The sailing race will be held," let l be the proposition "The lifesaving demonstration will go on."
and let t be the proposition "The trophy will be awarded."
Applying De Morgan's law on ¬(s∧l)→¬(r∨f), we obtain (¬s∨¬l)→(¬r∧¬f). Using ¬t and s→t, we get ¬s is true.
We get the conclusion "It rained" from the given hypotheses.
By modus ponens, (¬s∨¬l)→(¬r∧¬f) and ¬s∨¬l imply ¬r∧¬f and ¬r∧¬f implies ¬r using simplification.

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 th 89833

Added by Lee P.

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