### About Sets Part 2:

We sometimes use Venn diagrams to visually represent the relationship between two or more sets. The diagram is drawn with a rectangle that represents the universal set, or the set of all elements under consideration. We then draw circles to represent the various subsets of the universal set.

Test Objectives

- Demonstrate the ability to create a Venn diagram
- Demonstrate the ability to visually find the union of two or more sets
- Demonstrate the ability to visually find the intersection of two or more sets

#1:

Instructions: Determine if each statement is true or false.

U = {1,2,3,4,5,6,7}

A = {1,6,7} : B = {3,5,7}

a) A ∩ B = {5}

b) A ∪ B = {1,6,7,5,3}

c) A' = {5,3,4}

d) B' = {1}

e) B ⊂ A

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#2:

Instructions: Determine if each statement is true or false.

U = {George, Juan, Veronica, Sam, Tim, Charlie, Larry}

A = {George, Juan} : B = {Veronica, Tim} : C = {Sam, Tim}

a) A ∩ B = ∅

b) A ∪ B = {Veronica}

c) B ∩ C = {Tim}

d) C' = {Veronica, George, Juan}

e) A ∪ C = {George, Juan, Sam}

f) B ∪ C = {Veronica, Tim, Sam}

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#3:

Instructions: Find each from the Venn diagram.

a) U = ?

b) A = ?

c) B = ?

d) A ∩ B = ?

e) A ∪ B = ?

f) B' = ?

g) A' = ?

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#4:

Instructions: Draw a Venn diagram and determine if each statement is true or false.

U = {a,b,d,e,l,q,t,z}

A = {a,b,d} : B = {e,l,q} : C = {b}

a) A ∩ B = ∅

b) A ∩ C = {b}

c) A ⊂ C

d) C ⊂ A

e) C' = {a,d,e,l,q,t,z}

f) B' = {a,b,d,t,z}

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#5:

Instructions: Explain each and give an example.

a) intersection of two sets

b) union of two sets

c) complement of a set

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Written Solutions:

#1:

Solutions:

a) false

b) true

c) false

d) false

e) false

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#2:

Solutions:

a) true

b) false

c) true

d) true

e) false

f) true

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#3:

Solutions:

a) U = {1,2,3,5,7,8,9,11}

b) A = {1,3,9}

c) B = {2,5,7,9}

d) A ∩ B = {9}

e) A ∪ B = {1,2,3,5,7,9}

f) B' = {1,3,8,11}

g) A' = {2,5,7,8,11}

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#4:

Solutions:

a) true

b) true

c) false

d) true

e) true

f) true

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#5:

Solutions:

Your answer may vary: Let A = {1,2,3} and B = {3,4,5}

a) A ∩ B = {3} : The intersection of two sets is a set that contains all elements that are common to both

b) A ∪ B = {1,2,3,4,5} : The union of two sets is a set that contains all elements of both sets.

Your answer may vary: Let U = {1,2,3,4,5} and A = {1,2}

c) A' = {3,4,5} : The complement of a set is a set that contains all elements of U (universal set) that are not elements of the set under consideration.