Reference no: EM131113535

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:

    Use truth tables to determine whether each of the following pairs of propositions are logically equivalent.

(p ∨ q) ∧ ¬ q