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) false
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.
