chapter 2

1. CONCEPT OF SETS.

2. 1.Way of listing the elements of
Sets
 Put the elements in curly brackets..
{1,2,3,4}

3. 2.Specifying properties of sets
 i) intensional definition
A is the set whose members are the first four
days in a week.
 ii) extensional definition
A = {Sunday, Monday, Tuesday, Wednesday}

4. 3.Set membership , ∈
 ∈ means element of a.k.a relation
 x ∈ A means x is an element of set A
 A contains x A
x

5. 4.Empty set..
 Empty set is a set having no elements.

6. 5.Set of numbers (Z,N,etc....)


7. 6.Set Equality
Definition: Two sets are equal if and only if they
have the same elements.
Example:
{1,2,3} = {3,1,2} = {1,2,1,3,2}
Note: Duplicates don't contribute anything new to a
set, so remove them. The order of the elements in a
set doesn't contribute anything new.
 Example: Are {1,2,3,4} and {1,2,2,4} equal?
No!

9. 8.Subset
 Definition: A set A is said to be a subset of B if and only if every
element of A is also element of B. We use A ⊆ B to indicate A is a
subset of B.
Example: A={1,2,3} B ={1,2,3,4,5}
Is: A ⊆ B ? Yes.

10. POWER SET
 Power set of S is the set of all subsets of the
set S. The power of set S is denoted by P(S).
 Example:
What is the power set of set {3, 4, 5} ?
Solution:
P({3, 4, 5}) is the set of all subsets of {3, 4, 5}
P({3, 4, 5}) = {Ø, {3}, {4}, {5}, {3, 4}, {3, 5}, {4, 5}, {3, 4, 5}.

11. SET OPERATION
Union
A∪B
Both circle are shaded.

12. SET OPERATION
Intersection
A∩B
Only the portion shared by both circles are shaded.

13. OPERATION SET
 Disjoint set
If the intersection is empty, we called disjoint set.
U
A B

14. OPERATION SET
Set difference
A-B

15. OPERATION SET
Example set difference :
K = {a, b} L = {c, d} M = {b, d}
K –L ={a, b}
K –M ={a}
L – M= {c}
K–K=Ø
K–Ø=K
Ø–K=Ø

16. OPERATION SET
Set complimentary
Everything in universe that is not in the set

17. OPERATION SET
 Example :
U={A,B,C,D,E,F,G}
C={A,B,D,E,F}
C´={C,G}
U-C=C´

18. OPERATION SET
Characteristics of set.

19. GENERELISE UNION AND
INTERSECTION

20. GENERELISE UNION AND
INTERSECTION
Example :
Let A ={0,2,4,6,8}, B ={0,1,2,3,4} and C ={ 0,3,4,9}.
A∪B ∪C :
{0, 1 ,2, 3, 4, 6, 7, 8, 9}
A ∩ B∩ C :
{0}

21. CARTESIAN PRODUCT
 A and B are set
 A and B is set of all ordered pairs(a,b) where A∈a
and b∈B
Example:
Suppose A={1,2,} and B={2,3}. Then
A×B={(1,2),(1,3),(2,2),(2,3) }and
B×A={(2,1),(2,2),(3,1),(3,2)}