Solutions

  1. Answer:
    1. {{1}, {3}, {1, 3}, ∅}
    2. {{3}, {3, 4}, {3, 2}, {2, 3, 4}}
    3. {{1}, {1, 2}, {1, 3}, {1, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {1, 2, 3, 4}}
    4. {{2}, {3}, {4}, {2, 3}, {2, 4}, {3, 4}}
    5. {A ⊆ U : |A| = 2}

  2. Solution:

      1. Tp = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31}
      2. Tq = {1, 3, 9, 27, 81, . . . }
      3. Tr = {1, 3, 9, 27}
    2. r ⇒ q

  3. Answer: There are 23 = 8 subsets of U, allowing for the possibility of 28 nonequivalent propositions over U.

  4. Answer: Two possible answers: s is odd and (s − 1)(s − 3)(s − 5)(s − 7) = 0

  5. Solution: b and c