A+ Work

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