Intro to Set Theory
Operations
Cardinality
Venn Diagrams
100
List all elements in the following set:
A = The set of seasons in a year
{winter, spring, summer, fall}
100
Let A = {2, 4, 6, 8, 10} and B = (1, 2, 3, 4, 5, 6} Evaluate the following set operations:
A cup B =
A cap B =
A cup B = {1, 2, 3, 4, 5, 6, 8, 10}
A cap B = {2, 4, 6}
100
Determine the cardinality of the following sets:
A = {a, b, c, d, e}
B = {12, 0, 4, 22, 5, 31, 40}
C = {8}
|A| = 5
|B| = 7
|C| = 1
100
Represent the following operations using Venn diagrams:
a. A cup B
b. A cap B
200
Name all of the elements in the following set:
{ x | x in ZZ, 2 < x < 12}
{3, 4, 5, 6, 7, 8, 9, 10, 11}
200
Let A = {5, 6, 7}, B = {1, 2, 3, 7, 8, 9} and U =
{x | x in NN, x < 11}
Evaluate the following set operations:
a. A^C =
b. A - B =
c. B - A =
a. {1, 2, 3, 4, 8, 9, 10}
b. {5, 6}
c. {1, 2, 3, 8, 9}
200
Determine the cardinality of the following sets:
A = {x | x in NN, 10 < x < 20}
B = { x | x is a continent}
|A| = 9
|B| = 7
200
Represent the following set operations using Venn diagrams:
a. A^C
b. A - B
300
A = {green, blue}
List all possible subsets of A.
{ }, {green}, {blue}, {green, blue}
300
Let A = { x | x in NN, x < 12 }
and B = { x | x is a prime number, x < 12} .
Evaluate the following set operations:
A cap B =
A cup B =
A cap B = {2, 3, 5, 7, 11}
A cup B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}
300
True or False?
A = {a, b, c, d, e, f} and B = {1, 2, 3, 4, 5, 6}
a. A and B are equivalent sets.
b. A and B are equal sets.
a. True
b. False
300
Represent the following set operation using Venn diagrams:
a. (B cup C)'
400
Let A = {a, b, c}
a. List all possible subsets of A.
a. { }, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}
400
Let A = {10, 20, 30, 40}, B = {5, 10, 15, 20}, C = {20}, U = {1, 5, 10, 15, 20, 30, 35, 40}
Evaluate the following set operations:
a. B^C cap A =
b. (A - C) cup B =
a. {30, 40}
b. {5, 10, 15, 20, 30, 40}
400
Determine the cardinality of { a, b, c}
3
400
A survey of 39 adults revealed the following: 20 people like summer, 17 people like fall, 14 people like winter, 7 people like summer and fall, 6 people like summer and winter, 4 people like fall and winter, and 2 people like all three seasons.
How many people only like winter?
6 people only like winter
500
Let A = {95, 96, 97, 98, 99, 100}, B = {95, 97, 99}, and C = {100, 99, 98, 97, 96, 95}
True or False?
a. B subseteq A
b. B subset A
c. C is a subset of A
d. C is a proper subset of A
a. True
b. True
c. True
d. False
500
Let A = { x | x in ZZ, -4 < x < 4} , B = {x | x in NN, x < 5} , C =
{ x | x in ZZ, -5 < x < 5}
and U = {x | x in ZZ, -5 < x < 10}
Evaluate
(A - B) ^C cup C
{-4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
500
The cardinality of the set {4,8,12,16,..., 40}
10
500
A group of students were surveyed about their biggest fears. Results of the survey indicated that 30 were afraid of snakes, 18 were afraid of needles, and 24 were afraid of heights. 6 were afraid of snakes and needles, 7 were afraid of needles and heights, 14 were afraid of snakes and heights, and 5 were afraid of all three.
How many students were surveyed?
50 students