1. Let p represent a true statement, and q and r represent false statements. Find the truth value of the compound statement (∼ 𝒑 ∧∼ 𝒒) ∨ (∼ 𝒓 ∧ 𝒒).
2. Construct a truth table for the compound statement (𝒑 ∧∼ 𝒒) ∧ 𝒑
3. Use truth tables to decide if the pairs of statements are equivalent:
∼ (𝒑 β†’ 𝒒); 𝒑 ∧∼ 𝒒
4. For the statement β€œIf I finish reading this novel, then I’ll write a review”, write (a) the converse, (b) the inverse, and (c) the contrapositive in if . . . then form.
5. Determine the following argument is valid or invalid. If it is valid, give a proof. If it is invalid, give an assignment of truth values to the variables that makes the premises true and the conclusion false.

∼ 𝒑 β†’ 𝒒
Therefore, ∼ 𝒒

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Math Logic Problems
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