Section 2'3 Set Operations

1
Section 2.3 Set Operations

• Intersection of Sets
• The intersection of sets A and B, denoted by A n
  B, is the set of elements common to both A and B.
• A n B x x is in A and x is in B

2
Examples

• Let A 1, 4, 5, 7, B 2, 3, 4, 5, 6, and C
  3, 6, 9. Find
• a. A n B
• b. A n C

3
CHECK YOUR PROGRESS

• Let D0,3,8,9, E3,4,8,9,11 and
• F 0, 2, 6, 8. Find
• a. D n E
• b. D n F

4
Disjoint Sets

• Two sets are disjoint if their intersection is
  the empty set.

5
Union of Sets

• Union of Sets
• The union of sets A and B, denoted by A U B, is
  the set that contains all the elements that
  belong to A or to B or to both.
• A U B x x in A or x in B

6
EXAMPLE

• Let A 1, 4, 5, 7, B 2, 3, 4, 5, 6,
• and C 3, 6, 9.
• Find
• a. A U B
• b. A U C

7
CHECK YOUR PROGRESS

• Let D 0, 4, 8, 9, E 1, 5, 4, 7,
• and F 2, 6, 8.
• Find
• a. D U E
• b. D U F

8
Union and Intersection

• In mathematical problems that involve sets, the
  word "and" is interpreted to mean intersection.
  For instance, the phrase "the elements of A and
  B" means the elements of A n B.
• Similarly, the word "or" is interpreted to mean
  union. The phrase "the elements of A or B" means
  the elements of A U B.

9
EXAMPLE

• Write a sentence that describes the set.
• a. A U (B n C)
• b. J n K'
• Solution
• a. The set A U (B n C) can be described as the
  set of all elements that are in A, or are in B
  and C
• b. The set J n K' can be described as "the set
  of all elements that are in J and are not in K."

10
Venn Diagrams Involving Three Sets

• EXAMPLE
• Use Venn diagrams to determine whether
• A U (BnC) (A U B)nC for all sets A, B, and C.

11
Properties of Sets

• De Morgans Law
• For all sets A and B,
• (A U B)' A' n B' and (A n B)' A' U B'