Which of the following sentences are logical statements?

1. Which of the following sentences are logical statements?
   1. If x even divides y, then x is a factor of y
   2. If John does well in discrete math, then he will be an excellent programmer
   3. 2 is the only even prime number
   4. He is the best student in the class
2. Construct the truth tables for the following propositions:
   1. (p ∧ ¬ p) ∧ q
   2. (p ∨ q) ∧ (q ∨ ¬ p)
   3. p ∧ (q ∨ ¬ r)
   4. (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:

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

1. (p ∨ q) ∧ ¬ q

(¬ (p ∧ q)) ∨ q

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