(10 points) Determine whether the following argument is valid (prove if valid) or not (give a...

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(10 points) Determine whether the following argument is valid (prove if valid) or not (give a counterexample if invalid). First, translate each premise as a boolean proposition using a propositional variable for each atomic phrase. • Premise 1: If it is not cloudy or not windy, then we will visit the nearby town and do shopping. • Premise 2: If we visit the nearby town, then we will dine at a restaurant. • Premise 3: We did not dine at restaurant. . Conclusion: Therefore, It was cloudy. (10 points) Determine whether the following argument is valid (prove if valid) or not (give a counterexample if invalid). First, translate each premise as a boolean proposition using a propositional variable for each atomic phrase. • Premise 1: If it is not cloudy or not windy, then we will visit the nearby town and do shopping. • Premise 2: If we visit the nearby town, then we will dine at a restaurant. • Premise 3: We did not dine at restaurant. . Conclusion: Therefore, It was cloudy.