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Sets II Test

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

Sets II Test:

#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:

Solution:

a) false

b) true

c) false

d) false

e) false

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#2:

Solution:

a) true

b) false

c) true

d) true

e) false

f) true

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#3:

Solution:

a) U = {1,2,3,4,5,6,7,8,9,11}

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:

Solution:

a) true

b) true

c) false

d) true

e) true

f) true

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#5:

Solution:

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.

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