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SETS & COUNTING PRINCIPLE Flashcards | StudBud
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SETS & COUNTING PRINCIPLE
SETS & COUNTING PRINCIPLE
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1
Among 10 people, 5 like hockey (H) and 8 like soccer (S). Everyone liked at least one. How many like hockey AND soccer?
10
13
3
4
2
How many different possible outcomes can occur from spinning each once?
20
7
12
4
3
This symbol represents...
Cardinality
Universal Set
Intersection
Union
4
Find the number of outcomes from...
8
18
6
36
5
A pizza is made from one of each: 4 sizes, 3 crusts, 5 cheeses, 12 toppings. How many different pizzas are possible?
720
80
60
1440
6
The number of students playing varied sports is given. How many did not play any of these three sports?
31
30
4
3
7
Mr. Potato Head has 4 hats, 3 eyes, 4 mouths, and 2 shoes. How many potato heads are possible?
96
48
100
24
8
List ALL the subsets of { 1, 5 }.
{ 1 }, { 5 }, { 1, 5 }
∅, { 1 }, { 5 }
{ }, { 1 }, { 5 }, { 1, 5 }
∅, { }
9
Refer to the Venn Diagram. The number of students taking math or physics is
80
50
10
60
10
A code consists of 3 digits, but no digit can be repeated. How many codes are possible?
72
7,200
720
None of these
11
Find X ∪ (Y ∩ Z) given the following sets.
{ 2, 3, 4, 5, 7, 9 }
{ 3, 5 }
{ 2, 3, 4 }
{ 5, 7, 9}
12
Find Y ∩ Z given the following sets.
{ 5, 7, 9 }
{ 5 }
{ 2, 3, 4, 5, 7, 9 }
{ 3, 5 }
13
Skates are white, beige, pink, yellow, or blue. Sizes are 4, 5, 6, 7, or 8 with tassels, laces, or bells. How many?
100
25
75
50
14
How many subsets does the set {A, B, C} have?
3
8
4
6
15
What is the meaning of this symbol?
Union
Complement
Intersection
Universal Set
16
Identify the set shaded green.
B ∩ C
A' ∩ B ∩ C
A ∩ B ∩ C
B U C
17
True or False: The Empty Set a subset of Set A.
True
False
18
Perform the following operation with the given sets.
{ 1, 2, 3, 4, 5, 6, 7, 8 }
{ 3, 6, 7, 8 }
{ 1, 2, 3, 4, 6, 7, 8 }
{ 5, 6, 7, 8 }
19
Use the following information to determine the number of elements in C ∩ B .
8
11
3
19
20
Identify the set shaded green.
(A U C)' ∩ B
(A U C) ∩ B
A ∩ B ∩ C
(A ∩ B) ∩ (B ∩ C)
21
Identify the set shaded green.
A U B
(A ∩ B)'
(A U B)'
A' U B'
22
True or False: There are 8 outcomes from this tree diagram.
True
False
23
Which elements are in the intersection of Set A and Set B?
f, g, h
i, l, m, n
universal set
a, b, c, d, e
24
People at the mall were asked if they like Pop (P) or Rap (R). The results are shown in the Venn diagram below.
People who like rap.
People who do not like rap.
People who like pop or rap or both.
People who do not like pop.
25
For a five-digit alarm code, how many are possible if the first number cannot be 0 or 1 and the last cannot be odd?
400,000
40,000
10,000
100,000
26
Given the information below, how many students take both Chemistry and Physics?
9
20
14
6
27
How many outcomes are there from this tree diagram?
6
2
12
3
28
True or False: This is a symbol for an empty set.
False
True
29
People at the mall were asked if they like Pop (P) or Rap (R). The results are shown in the Venn diagram below.
People who do not like pop or rap.
People who like pop or rap or both.
People who only like pop.
People who like both pop and rap.
30
NC issues standard license plates with 3 letters followed by 4 numbers. How many possible plates are there?
17,576
10,000,000
260
175,760,000
31
Name the set shaded grey.
(A ∩ B)
(A ∩ B)'
(A U B)'
the universal set
32
Which statement below is TRUE?
B is a subset of A.
A is a subset of B.
33
50 students were surveyed. Using the results, how many like math and science?
3
5
18
33
34
What is this called?
A Van Diagram
A Set Diagram
A Vonn Diagram
A Venn Diagram
35
Name the set shaded yellow.
B'
A ∩ B
A'
A ∪ B
36
A quiz has 5 multiple-choice questions, each with 4 choices. How many answer sets are there with all questions answered?
1024
625
9
20
37
How many salads are possible if choosing 1 from each: 2 types of lettuce, 4 veggies, and 7 dressings.
42
56
13
None of these
38
If A = { 1, 3, 5, 7, 9 } and B = { 2, 3, 5, 7 }, what is A ∪ B ?
{ 3, 5, 7 }
{ 2, 3, 5, 7, 9 }
{ 2, 3, 5, 7 }
{ 1, 2, 3, 5, 7, 9 }
39
You are buying a car. You have options of 2 body styles, 5 colors, and 3 models. How many choices are possible?
13
21
16
30
40
A theater sells 4 sizes of popcorn with 3 types of toppings. How many different buckets are sold?
64
12
7
27
41
The number of elements in each set is shown. How many elements are in
A
∩ B
?
21
4
5
1
42
Which of the following describes the shaded part in the diagram here?
B
A'
A
B'
43
Represented are the number of elements in each space. Determine the number of elements in C
U
T.
83
45
38
23
44
From the Venn diagram shown, what is the set T' ?
{blair, erin, francis, ira}
{casey, drew, jade}
{alex, blair, erin, francis, hunter, ira}
{alex, blair, erin, francis, glen, hunter, ira}
45
Refer to the Venn Diagram. The number of students currently taking math but not physics is
45
10
40
50
46
What set operation results in ∅ ?
A ∩ B
B ∩ D
A ∩ C
B ∪ D
47
True or False: Set A is a subset of Set B.
True
False
48
How many license plates can be made with 1 letter followed by 5 digits if there are no repeats?
604,800
75,348,000
2,600,000
786,240
49
Name the set shaded green.
A ∩ B
B'
A U B
A'
50
Find X
∪
Y given the following sets.
{ 3, 5 }
{ 7, 9 }
{ 2, 3, 5, 7, 9 }
{ 2, 3, 4, 5, 7, 9 }
51
A quiz contains 5 true/false questions. How many outcomes are possible if every question is answered?
None of these
32
100
10
52
What is the number of outcomes if you buy a white, black, or gold iphone and then choose one of eleven phone cases?
330
10
1000
33
53
How many outcomes are possible when rolling 2 dice and tossing 2 coins?
122
14
12
144
54
True or False: The shading in this Venn Diagram represents A U B .
True
False
55
True or False: Set C is a subset of Set A.
True
False
56
How many choices are there when picking an outfit if you wear one each: 10 tops, 3 pants, and 2 shoes.
30
20
15
60
57
How many subsets are there for the set { f, g, h, i, j } ?
5 x 2 = 10 subsets
5 subsets
52 = 25 subsets
25 = 32 subsets
58
How many lunch outcomes from one each of ham or turkey or PB&J sandwich, Doritios or Cheetos, and then apple or orange ?
2
3
12
7
59
If one bagel and one cream cheese flavor are chosen, how many choices are there?
12
6
22
120
60
This tree diagram is for what events?
tossing a coin four times
tossing a coin twice
none of the above
tossing a coin once
61
The ice cream shop offers 31 flavors. You order a double scoop cone. How many different cones are possible?
961
960
62
900
62
Which of the following sets is NOT a subset of { 1, 2, 3, 4, 5 } ?
{ }
{ 1, 2, 3, 4, 5 }
{ 2, 4, 5 }
{ 1, 2, 6 }
63
What is the size of the sample space of rolling a die, spinning this spinner, and flipping a coin?
20
15
94
84
64
How many passwords can be made by choosing two numbers from 1 through 6 followed by one letter of the alphabet?
926
936
916
906
65
There are 3 meats, 5 vegetables, and 2 breads. How many meals are there with one of each?
10
None of these
15
33
66
How many students are in the 12th Grade?
125
100
101
105
67
A code consists of 2 digits followed by 1 letter. How many codes are possible?
2,600
5,200
520
260
68
Find the number of elements in the set.
1
3
2
4
69
Identify the set shaded green.
B ∩ (A U C)'
B
(A U C)'
B'
70
In an embassy with 65 employees, 47 speak German, 35 Speak Italian, and 20 speak both. How many speak neither?
4
2
1
3
71
If the universal set is U = {a, b, c, d, e, f, g} and Y = {a, b, c, d}, then how many elements are in Y' ?
2
11
5
3
72
Name the set shaded pink.
A
(A ∩ B)'
A ∩ B'
B'
73
What is the number of outcomes if you flip a coin and then pick a state?
100
50
75
25
74
E = {x|x is an even number} and O = {x|x is an odd number}. Which statement is TRUE?
E ∪ O = ∅
E ∩ O = ∅
Neither is true.
Both are true.
75
What is the size of the sample space given the following information?
9
3
27
6
