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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. 
      
      1. T_p = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31}
      2. T_q = {1, 3, 9, 27, 81, . . . }
      3. T_r = {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.
   
   
5. Answer: Two possible answers: s is odd and (s − 1)(s − 3)(s − 5)(s − 7) = 0
   
   
7. Solution: b and c