1.6.6: Chapter Test
- Page ID
- 129507
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1. Determine whether the following collection describes a well-defined set: "A group of small tomatoes."
Classify each of the following sets as either finite or infinite.
2. \(\{1,5,9, \ldots\}\)
3. \(\{c \mid c\) is a cat \(\}\)
4. \(\{1,2,3, \ldots, 1000\}\)
5. \(\{s, m, i, l, e\}\)
6. \(\left\{m \in \mathbb{N} \mid m=n^2\right.\) where \(n\) is a natural number \(\}\)
Use the sets provided to answer the following questions: \(U=\{31,32,33, \ldots, 50\}, A=\{35,38,41,44,47,50\}, B=\{32,36,40,44,48\} \text {, and } C=\{31,32,41,42,48,50\}\).
7. Find \(A\) or \(B\).
8. Find \(B\) and \(C\).
9. Determine if set \(A\) is equivalent to, equal to, or neither equal nor equivalent to set \(C\). Justify your answer.
10. Find \(n(A \cup C)\).
11. Find \(A \cap(B \cap C)\).
12. Find \((A \cup B)^{\prime} \cap C\).
13. Find \(\left(A \cap B^{\prime}\right) \cup C\).
Use the Venn diagram below to answer the following questions.
14. Find \(B^{\prime}\).
15. Find \(A \cup B\).
16. Find \(A \cap B^{\prime}\).
17. Draw a Venn diagram to represent the relationship between the two sets: "All flowers are plants."
For the following questions, use the Venn diagram showing the blood types of all donors at a recent mobile blood drive.
Find the number of donors who were \(\mathrm{O}^{-}\); that is, find \(n\left(\left(A \cup B \cup R h^{+}\right)^{\prime}\right)\).
Find the number of donors who were \(\mathrm{A}^{+}\)or \(\mathrm{B}^{+}\)or \(\mathrm{AB}^{+}\).
Use Venn diagrams to prove that if \(A \subset B\), then \(A \cap B=A\).