1. Which of the following sentences are logical statements?
If x even divides y, then x is a factor of y
If John does well in discrete math, then he will be an excellent programmer
2 is the only even prime number
He 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