1.7.7: Chapter Test

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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, \ldots \}/**/

/**/\{ c|c{\text{ is a cat}}\}/**/

/**/\{ 1,2,3, \ldots ,1000\}/**/

/**/\{s,m,i,l,e\}/**/

/**/\{ m \in \mathbb{N}|m = {n^2}\,{\text{where}}\,n\,{\text{is}}\,{\text{a}}\,{\text{natural}}\,{\text{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\}/**/, and /**/C = \{ 31,32,41,42,48,50\}/**/.

Find /**/A\,{\text{or}}\,B/**/.

Find /**/B\,{\text{and}}\,C/**/.

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)' \cap C/**/.

13.

Find /**/(A \cap {B^\prime }) \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.
$A three-set Venn diagram of A, B, and Rh plus overlapping one another is given. The total number of donors equals 128. Set A shows 7; Set B shows 5; Set Rh plus shows 47. Overlapping of sets A and B shows 4, overlapping of sets B and Rh plus shows 12, and overlapping of A and Rh plus shows 40. Overlapping of A, B, and Rh plus shows 3.$

18.

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

19.

Find the number of donors who were /**/\text{A}{^ + }\,{\text{or}}\,\text{B}{^ + }\,{\text{or}}\,\text{AB}{^ + }/**/.

20.

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

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Chapter Test