## Try It Now

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

### Exercises

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

- Over the universe of positive integers, define:
(

p*n*):*n*is prime and*n*< 32.*q*(*n*):*n*is a power of 3.*r*(*n*): n is a divisor of 27.

- What are the truth sets of these propositions?
- Which of the three propositions implies one of the others?

- If
*U*= {0, 1, 2}, how many propositions over U could you list without listing two that are equivalent? - Suppose that
*s*is a proposition over {1,2, . . . , 8}. If*T*= {1,3, 5, 7}, give two examples of propositions that are equivalent to_{s}*s*. - Let the universe be ℤ, the set of integers. Which of the following propositions are equivalent over Z?
: 0 <

a*n*^{2}< 9*b*: 0 <*n*^{3}< 27*c*: 0 <*n*< 3

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

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