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1. Which of the following sentences are logical statements?If x even divides y, then x is a factor of yIf John does well in discrete math, then he will be an excellent programmer2 is the only even prime numberHe is the best student in the class
2. Construct the truth tables for the following propositions:(p ∧ ¬ p) ∧ q(p ∨ q) ∧ (q ∨ ¬ p)p ∧ (q ∨ ¬ r)(p ∧ q) ∨ (p ∧ r)
3. Refer to the propositions in problem 2. For each of them, indicate whether it is a tautology, a contradiction or neither.
4. Use truth tables to determine whether the following is valid argument:
p → q
q → p
∴ p ∨ q
Use truth tables to determine whether each of the following pairs of propositions are logically equivalent.(p ∨ q) ∧ ¬ q
¬ q ∧ (q ∨ p)(¬ (p ∧ q)) ∨ q
(¬ p ∧ ¬ q) ∨ q
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