1.6.6: Chapter Test

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    Chapter Test

    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.

    A two-set Venn diagram of A and B is given. Set A shows e, l while set B shows g. The intersection of the sets shows o, d. Outside sets A and B, n is shown. The union of the sets A and B shows (g, o, l, d, e, n).

    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.

    A three-set Venn diagram of A, B, and Rh plus overlapping one another is given. The total number of donors equals 128. Set A shows 7; Set B shows 5; Set Rh plus shows 47. Overlapping of sets A and B shows 4, overlapping of sets B and Rh plus shows 12, and overlapping of A and Rh plus shows 40. Overlapping of A, B, and Rh plus shows 3.

    Exercise \(\PageIndex{18}\)

    Find the number of donors who were \(\mathrm{O}^{-}\); that is, find \(n\left(\left(A \cup B \cup R h^{+}\right)^{\prime}\right)\).

    Exercise \(\PageIndex{19}\)

    Find the number of donors who were \(\mathrm{A}^{+}\)or \(\mathrm{B}^{+}\)or \(\mathrm{AB}^{+}\).

    Exercise \(\PageIndex{20}\)

    Use Venn diagrams to prove that if \(A \subset B\), then \(A \cap B=A\).

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