Discrete Structures - Old Questions

2. State division and remainder algorithm. Suppose that the domain of the propositional function P(x) consists of the integers 0, 1, 2, 3 and 4. Write out each of following propositions using disjunctions, conjunctions and negations.        [4+6]

    a. ∃x P(x)

    b. ∀x P(x)

    c. ∃x ¬P(x)

    d. ∀x ¬P(x)

    e. ¬∃x P(x)

    f. ¬∀x P(x)