## Try It Now

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

### Exercises

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

2. Over the universe of positive integers, define:

p
(n): is prime and n < 32.
q(n): n is a power of 3.
r(n): n is a divisor of 27.
1. What are the truth sets of these propositions?
2. Which of the three propositions implies one of the others?

3. If U = {0, 1, 2}, how many propositions over U could you list without listing two that are equivalent?

4. Suppose that sis a proposition over {1,2, . . . , 8}. If Ts= {1,3, 5, 7}, give two examples of propositions that are equivalent to s.

5. Let the universe be ℤ, the set of integers. Which of the following propositions are equivalent over Z?

a
: 0 < n2 < 9
b: 0 < n3 < 27
c: 0 < n < 3

Source: Al Doerr and Ken Levasseur, http://faculty.uml.edu/klevasseur/ads-latex/ads.pdf This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License.