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
1. 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
5. Give an example of a proposition that contains at least three independent variables and at least five operations. Provide the truth table for that proposition. Is it a tautology,a contradiction or neither? Explain.
6. Describe the differences between black-box testing and white-box testing. Which strategy do you feel to be more useful? Why? (Name and describe at least one type of black or white box test as part of your discussion).