1. Objective- To use intersection and union to simplify problems involving sets.
Operations with Sets
A = { 1, 2, 3 ,4, 5}
B = { 2, 4, 6, 8, 10}
C = { 5, 6, 7, 8}
Intersection ( )
( and )
- the elements which are
common to both sets.
{ 2, 4}
1) A B =
4) (A B) C
{ 2, 4}
{ 5, 6, 7, 8}
{ 6, 8}
2) B C =
{ }
or “empty set”
{ 5 }
3) A C =
or O
or “null set”

2. Operations with Sets
A = { 1, 2, 3 ,4, 5}
B = { 2, 4, 6, 8, 10}
C = { 5, 6, 7, 8}
Union ( )
( or )
- the combined set of elements from
two sets with no duplication of elements.
{ 1, 2, 3, 4, 5, 6, 8, 10}
1) A B =
{ 2, 4, 5, 6, 7, 8, 10}
2) B C =
{ 1, 2, 3, 4, 5, 6, 7, 8}
3) A C =

3. A = { 1, 2, 3 ,4, 5}
B = { 2, 4, 6, 8, 10}
C = { 5, 6, 7, 8}
Draw Venn Diagrams to represent...
1) A B
2) A B A B 1 2 3 6 8 4 5 10

4. A = { 1, 2, 3 ,4, 5}
B = { 2, 4, 6, 8, 10}
C = { 5, 6, 7, 8}
Draw Venn Diagrams to represent...
1) A B
2) A B A B A B 1 2 3 6 2 1 6 8 3 8 4 4 5 10 5 10

5. A = { 1, 2, 3 ,4, 5}
B = { 2, 4, 6, 8, 10}
C = { 5, 6, 7, 8}
Draw Venn Diagrams to represent...
1) A B
2) A B A B A B 1 2 3 6 2 1 6 8 3 8 4 4 5 10 5 10
Note: The only difference is the shading.

6. Number Line Graphs of Inequalities
Intersections
Unions
x < x < 3
x < x < 3
{ x : x < 3 }
{ x : x < 5 }
x < x > 3
x < x > 3
{ x : 3 < x < 5 }
{ x : x = Any Real Number }

7. Number Line Graphs of Inequalities
Intersections
Unions
x > x < 3
x > x < 3
{ }
{ x : x < 3 or x > 5 }
x > x > 3
x > x > 3
{ x : x > 5 }
{ x : x > 3 }