# Expert Answers

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

Construct the truth tables for the following propositions:

(p ∧ ¬ p) ∧ q

(p ∨ q) ∧ (q ∨ ¬ p)

p ∧ (q ∨ ¬ r)

(p ∧ q) ∨ (p ∧ r)

Refer to the propositions in problem 2. For each of them, indicate whether it is a tautology, a contradiction or neither.

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

(¬ (p ∧ q)) ∨ q

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

Construct the truth tables for the following propositions:

(p ∧ ¬ p) ∧ q

(p ∨ q) ∧ (q ∨ ¬ p)

p ∧ (q ∨ ¬ r)

(p ∧ q) ∨ (p ∧ r)

Refer to the propositions in problem 2. For each of them, indicate whether it is a tautology, a contradiction or neither.

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

(¬ (p ∧ q)) ∨ q

You'll get a 25.5KB .DOCX file.