Try It Now

Work these exercises to see how well you understand this material.

Exercises

  1. If U = ℘ ({1, 2, 3, 4}), what are the truth sets of the following propositions?
    1. A ∩ {2, 4} = ∅.
    2. 3 ∈ A and 1 ∉ A.
    3. A ∪ {1} = A.
    4. A is a proper subset of {2, 3, 4}.
    5. |A| = |Ac|.

  2. Over the universe of positive integers, define:

    p
    (n): is prime and n < 32.
    q(n): n is a power of 3.
    r(n): n is a divisor of 27.
    1. What are the truth sets of these propositions?
    2. Which of the three propositions implies one of the others?

  3. If U = {0, 1, 2}, how many propositions over U could you list without listing two that are equivalent?

  4. Suppose that sis a proposition over {1,2, . . . , 8}. If Ts= {1,3, 5, 7}, give two examples of propositions that are equivalent to s.

  5. Let the universe be ℤ, the set of integers. Which of the following propositions are equivalent over Z?

    a
    : 0 < n2 < 9
    b: 0 < n3 < 27
    c: 0 < n < 3

 


Source: Al Doerr and Ken Levasseur, http://faculty.uml.edu/klevasseur/ads-latex/ads.pdf
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