Prove that each argument is valid by replacing each proposition in the hypotheses with a variable to obtain the form of the argument, and define all variables in your answer. Then use the rules of inference to prove that the form (~ the logical steps from hypotheses to conclusion) is valid. Hypotheses: a. If it was not foggy or it didn't rain (or both), then the race was held and there was a trophy ceremony. b. The trophy ceremony was not held. Conclusion: ∴ It rained.
Prove that each argument is valid by replacing each proposition in the hypotheses with a variable to obtain the form of the argument, and define all variables in your answer. Then use the rules of inference to prove that the form (~ the logical steps from hypotheses to conclusion) is valid.
Hypotheses:
a. If it was not foggy or it didn't rain (or both), then the race was held and there was a trophy ceremony.
b. The trophy ceremony was not held.
Conclusion:
∴ It rained.
Given:
Hypotheses:
a. If it was not foggy or it didn't rain (or both), then the race was held and there was a trophy ceremony.
b. The trophy ceremony was not held.
Conclusion:
It rained.
We have to prove the given argument is valid.
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