## Try It Now

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

### Solutions

- Answer:

- {{1}, {3}, {1, 3}, ∅}
- {{3}, {3, 4}, {3, 2}, {2, 3, 4}}
- {{1}, {1, 2}, {1, 3}, {1, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {1, 2, 3, 4}}
- {{2}, {3}, {4}, {2, 3}, {2, 4}, {3, 4}}
- {
*A*⊆*U*: |*A*| = 2}

- Solution:

*T*= {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31}_{p}*T*= {1, 3, 9, 27, 81, . . . }_{q}*T*= {1, 3, 9, 27}_{r}

- r ⇒ q

- Answer: There are 2
^{3}= 8 subsets of*U*, allowing for the possibility of 2^{8}nonequivalent propositions over*U*. - Answer: Two possible answers:
*s*is odd and (*s*− 1)(*s*− 3)(*s*− 5)(*s*− 7) = 0 - Solution:
*b*and*c*