Set Theory for SOAR

Intro to Set Theory

100

List all elements in the following set in roster form:

A = The set of seasons in a year

{winter, spring, summer, fall}

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}

300

Given A = {green, blue}  

a. How many possible subsets of A?

b. List all possible subsets of A. 

a. 2^{2 =} 4

b. { }, {green}, {blue}, {green, blue}

400

Let A = {a, b, c}  

a. How many possible subsets of A?

b. How many possible proper subsets of A?

c. List the possible subsets of A

a. 2³ = 8

b. 2³ - 1 = 7

c. { }, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}

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

e.  99 in A 

a. True

b. True

c. True

d. False

e. True

Operations

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}

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^' =  

b.  A^' cap B =  

c.  B^' cup A^' = 

a. {1, 2, 3, 4, 8, 9, 10}

b. {1,2,3,8,9}

c. {1, 2, 3, 4, 5, 6, 8, 9, 10} 

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}

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^' cap A =  

b.  (A cap C^') cup B = 

a. {30, 40}

b. {5, 10, 15, 20, 30, 40}

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) ^' cup C

{-4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

Cardinality and Empty Set

100

Determine the cardinality of the following sets: 

A = {a, b, c, d, e}

B = {12, 0, 4, 22, 5, 31, 40}

C = {8}

n(A) = 5

n(B) = 7

n(C) = 1

200

Determine the cardinality of the following sets:

A =  {x | x in NN, 10 < x < 20} 

B = { x | x is a continent}

n(A) = 9

n(B) = 7 

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

400

For Sets in General, answer  A, U, or O/ 

a.  A cap O/ 

b.  A cap U 

c.  A cap A^' 

O/

A

O/

500

For Sets in General, answer  A, U, or O/ 

a.  A cup O/ 

b.  A cup U 

c.  A cup A^' 

A

U

U

Venn Diagrams

100

Represent the following operations using Venn diagrams:

a.  A cup B 

b.  A cap B 

200

Represent the following set operations using Venn diagrams:

a.  A^" 

b.  A cap B^' 

300

Represent the following set operation using Venn diagrams: 

a.  (B cup C)' 

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

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  

Miscellaneous

100

Identify the pattern in the list of numbers. Then use this pattern to find the next number. 

4, 10, 14, 24, 38, 62, ___

100

200

Identify the pattern in the list of numbers. Then use this pattern to find the next number. 

3, 7, 15, 31, 63, __

add double of what was added previously

127

300

You decide you need a new computer. The cost of the computer is $816. However, the store also offers a rent to own option which will cost $39 per week for 24 weeks. How much more will the rent to own option cost after you have made all of the payments?

39 x 24 =936

936 - 816 =120

You will pay $120 more for rent to own.

400

According to a survey, 45,274,865 people can speak a language other than their native  language.  Round this number to the nearest, 

a. hundred, 

b. hundred thousand, 

c. million

a. 45, 274, 900

b. 45, 300, 000

c. 45, 000, 000

500

Each day a small business owner sells 200 pizza slices at $1.50 per slice and 85 sandwiches at $3.50 each. Business expenses come to $60 per day.  What is the owner's profit for a ten-day period? 

200 x 1.50 =$300 for pizza

85 x 3.50 = $297.50 for sandwiches

10 (300 + 297.50) = $5975 Income for 10 days

10 x 60 = $600 Expenses for 10 days

5975 - 600 = $5375 profit for a ten-day period