2.3 Completed Notes - University of South Carolinapeople.math.sc.edu/lanema/math221/Completed...
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2.3 Completed Notes
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2.3: Other Set Operations
Definition: If A and B are sets, the intersection of A and B, denoted A ∩ B, is the set of elements that are in both A and B. That is,
An intersection can be thought of in the following manner. The shaded region is A ∩ B:
Examples:{1, 2, 3, 4} ∩ {2, 4, 6, 8} =
{x2 | x ∈ } ∩ {1, 2, ..., 20} =
{1, 2} ∩ {1, 2, 3} =
{1, 2} ∩ {3, 4} =
∅ ∩ {1,2} =
UBA
Definition: If A and B are sets, the union of A and B, denoted A ∪ B, is the set of elements that are in either A or B. That is,
A union can be thought of in the following manner. The shaded region isA ∪ B:
Examples:{1, 2, 3, 4} ∪ {2, 4, 6, 8} =
{x2 | x ∈ } ∪ {1, 2, ..., 20} =
{1, 2} ∪ {1, 2, 3} =
{1, 2} ∪ {3, 4} =
∅ ∪ {1,2} =
UBA
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UBA
Definition: If A and B are sets, the set difference of B and A (or relative complement of A relative to B), denoted A − B and read "A set minus B", is the set of elements that are in A but not in B. That is,
A set difference can be thought of in the following manner. The shaded region is A − B:
Examples:
{1, 2, 3, 4} − {2, 4, 6, 8} =
{1, 2, ..., 20} − {x2 | x ∈ } =
{1, 2} − {1, 2, 3} =
{1, 2} − {3, 4} =
∅ − {1,2} =
Example: Draw the Venn Diagram for A ∪ B.
U
A B
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Example: Draw the Venn Diagram for A ∪ B.
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A B
Example: Draw the Venn Diagram for A ∩ B.
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A B
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Example: Draw the Venn Diagram for A ∩ B.
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A B
Example: Draw the Venn Diagram for A − B.
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A B
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Example: Draw the Venn Diagram for A − B.
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A B
Example: Draw the Venn Diagram for (A ∩ B) ∪ C.
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A B
C
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Example: Draw the Venn Diagram for (A ∪ B) − C.
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A B
C
Example: Draw the Venn Diagram for A ∩ (B ∪ C).
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A B
C
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Problem 1: Draw the Venn Diagram for A ∩ B.
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A B
Problem 2: Draw the Venn Diagram for B − A.
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A B
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Problem 3: Draw the Venn Diagram for A ∩ B.
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A B
Problem 4: Draw the Venn Diagram for A ∪ B.
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A B
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Problem 5: Draw the Venn Diagram for (A ∩ B) ∩ C.
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A B
C
Problem 6: Draw the Venn Diagram for A ∩ (B ∪ C).
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A B
C
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Problem 7: Draw the Venn Diagram for A − (B ∪ C).
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A B
C
Problem 8: Draw the Venn Diagram for (A − B) ∪ C.
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A B
C
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Problem 9: Draw the Venn Diagram for A ∪ (B ∪ C).
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A B
C
Problem 10: Draw the Venn Diagram for A ∩ (B ∩ C).
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A B
C
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2.3 Completed Notes
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