Mathematics
SET
-is a collection of distinct, well-
defined objects forming a group.
-has definite Criterion
-each object in a set is called a
member or ELEMENT of a set
ELEMENT symbol ∈
not an element symbol ∉
THINGS TO REMEMBER
1.The set is denoted by a CAPITAL
LETTER
Ex. Set of Natural Numbers = N
2.Elements are written inside a pair of
brackets {}
Ex. N = {1, 2, 3, 4, 5, ...}
3. Elements and not an element
Ex. 3 N but -3 ∉ N
4. Elements are separated by commas
5. If elements are represented by letters,
use small
letters
6. The order of elements in a set does not
matter.
CARDINALITY OF SETS
The cardinality of a set is the total
number of
unique elements in a set.
Denoted as n(A) or | A |
example: Find the cardinality
1. Z = { 1, 3, 5, 7, 9 }
n(Z) = 5
2. E = { 2, 4, 6, 6, 8, 2 } n(E) = 4
SUBSETS
A subset is a set whose elements are all
members of another set. The symbol "⊆"
means "is a subset of" and ⊆ is not a
subset of.
example: A = { 2, 4, 6, 8 }
B = { 2, 4 }
B ⊆ A
C ⊆A
C = { 4 , 6 }
D = { 4, 5, 6}
D ⊆ A
HOW TO DETERMINE THE
NUMBER OF SUBSETS?
If a set has “n” elements, then the
number of subset of the given set is 2n
example: A = { 1, 2, 3 }
number of subsets of A = 2³
A = {}, {1}, {2}, {3}, {1,2}, {1,3},
{2,3}, {1,2,3}
WHAT DOES THE CONNECTION OF
SETS A AND B?
B is a subset of A or B ⊆ A
EMPTY SET- (no elements)
An empty set is a set that does not
contain any
elements. It is also called a
”null set”
-It is a subset of any set
