1.7 Chapter 1 Practice Test

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1.7 Chapter 1 Practice Test

Chapter Test

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.
$\{1, 5, 9, \dots\}$
$\{c | c \text{ is a cat }\}$
$\{1, 2, 3, \dots, 1000\}$
$\{s, m, i, l, e\}$
$\{m \in \N | m = n^2 \text{ where } n \text{ is a natural number }\}$
Use the sets provided to answer the following questions: $U = \{31, 32, 33, \dots, 50\}$ , $A = \{35, 38, 41, 44, 47, 50\}$ , $B = \{32, 36, 40, 44, 48\}$ , and $C = \{31, 32, 41, 42, 48, 50\}$ .
Find $A \cup B$ .
Find $B \cap C$ .
Determine if set $A$ is equivalent to, equal to, or neither equal nor equivalent to set $C$ . Justify your answer.
Find $n(A \cup C)$ .
Find $A \cap (B \cap C)$ .
Find $(A \cup B)' \cap C$ .
Find $(A \cap B') \cup C$ .
Use the Venn diagram below to answer the following questions.

Figure [Number] 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).
Find $B'$ .
Find $A \cup B$ .
Find $A \cap B'$ .
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.

Figure [Number] 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.
Find the number of donors who were $O-$ ; that is, find $n((A \cup B \cup Rh+)')$ .
Find the number of donors who were $A+$ or $B+$ or $AB+$ .
Use Venn diagrams to prove that if $A \subset B$ , then $A \cap B = A$ .