Discrete Structures

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  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:

    p → q
    q → p
    ∴ p ∨ q

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

  6. (p ∨ q) ∧ ¬ q
    ¬ q ∧ (q ∨ p)

  7. (¬ (p ∧ q)) ∨ q
    (¬ p ∧ ¬ q) ∨ q

 

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