Try It Now

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

Exercises

  1. Let A = {0, 2, 3}, B = {2, 3}, C = {1, 4}, and let the universal set be U = { 0, 1 , 2 , 3 , 4 }. List the elements of:
    1. A × B
    2. B × A
    3. A × B × C
    4. U × ∅
    5. A × Ac
    6. B2
    7. B3
    8. B × \wp(B)

  2. List all two-element sets in \wp(\left \{ a, b, c, d \right \}).

  3. How many singleton (one-element) sets are there in \wp (A) if |A| = n ?

  4. Let A = {+ , −} and B = {00, 01, 10, 11}.
    1. List the elements of A × B
    2. How many elements do A4 and (A × B)3 have?

  5. Let A and B be nonempty sets. When are A × B and B × A equal?

 

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