Exam 2: Propositional Logic: Syntax and Semantic

Construct a complete truth table for each of the following arguments. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, specify a counterexample. -A / A • ∼A

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -[(Y ⊃ ∼Y) ⊃ (B ⊃ ∼B)] ⊃ [( B $\lor$ Y) ≡ (∼B $\lor$ ∼Y)]

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -X $\lor$ [A • (B ⊃ Y)]

Construct a complete truth table for each of the following arguments. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.) -∼A ≡ B (∼A $\lor$ B) ⊃ C / C

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -∼Q $\lor$ (∼X $\lor$ Q)

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -(Z $\lor$ ∼A) ≡ [(A $\lor$ ∼Z) ⊃ (X ≡ ∼X)]

construct a complete truth table for each of the following propositions. Then, using the truth table, classify each proposition as a tautology, a contingency, or a contradiction. Justify your answers by appeal to the meanings of those terms. -(G • ∼G) ⊃ (G $\lor$ ∼G)

Construct a complete truth table for each of the following arguments. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, specify a counterexample. -M ⊃ N O ⊃ M ∼N M ⊃∼O / M