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Chapter Test

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 , … }
3 .
{ c | c  is a cat }
4 .
{ 1 , 2 , 3 , … , 1000 }
5 .
{ s , m , i , l , e }
6 .
{ m ∈ N | m = n 2 where n is a natural number }
Use the sets provided to answer the following questions: U = { 31 , 32 , 33 , … , 50 } , A = { 35 , 38 , 41 , 44 , 47 , 50 } , B = { 32 , 36 , 40 , 44 , 48 } , 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 ∪ C ) .
11 .
Find A ∩ ( B ∩ C ) .
12 .
Find ( A ∪ B ) ′ ∩ C .
13 .
Find ( A ∩ B ′ ) ∪ 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 ′ .
15 .
Find A ∪ B .
16 .
Find A ∩ B ′ .
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 O − ; that is, find n ( ( A ∪ B ∪ R h + ) ′ ) .
19 .
Find the number of donors who were A + or B + or AB + .
20 .
Use Venn diagrams to prove that if A ⊂ B , then A ∩ B = A .