Set: A Set is a collection or group of objects or elements or members.
A Set is said to contain its elements.
Notation: A Set S can be written in following different ways:
S = {..., -2, 0, 2, ...}
S = {x | x = 2n, n ∈ Z}
S = {x : x = 2n, n ∈ Z}
It is read as " a set of all x's such that x is twice an integer".
If x is a member or element of the set S, we write x ∈ S If x is not a member or element of the set S, we write x ∉ S
Universal Sets: It's a set that contains everything. Well, not exactly everything.
Everything that is relevant to the problem you have.
Common Universal Sets:
A Set is said to contain its elements.
Notation: A Set S can be written in following different ways:
S = {..., -2, 0, 2, ...}
S = {x | x = 2n, n ∈ Z}
S = {x : x = 2n, n ∈ Z}
It is read as " a set of all x's such that x is twice an integer".
If x is a member or element of the set S, we write x ∈ S If x is not a member or element of the set S, we write x ∉ S
Universal Sets: It's a set that contains everything. Well, not exactly everything.
Everything that is relevant to the problem you have.
Common Universal Sets:
Element v/s Subset: Sets can be subsets and elements of other sets.
Example:
If S = {2, 3, {2}, {4}}
Then
2 ∈ S
3 ∈ S
{2} ∈ S
{4} ∈ S
4 ∉ S
{3} ∉ S
{2} ⊂ S
{3} ⊂ S
{{2}} ⊂ S
{{4}} ⊂ S
{4} ⊄ S
{{3}} ⊄ S
Cardinality: Cardinality of a set A is defined as the number of elements in the set A, and is written as |A|.
Set Operations:
A ∪ B = {x | x ∈ A or x ∈ B}
A ∪ B = {x | x ∈ A and x ∈ B}
A - B = {x | x ∈ A or x ∉ B}
A X B = {(x, y) | x ∈ A or y ∈ B}
Example:
If S = {2, 3, {2}, {4}}
Then
2 ∈ S
3 ∈ S
{2} ∈ S
{4} ∈ S
4 ∉ S
{3} ∉ S
{2} ⊂ S
{3} ⊂ S
{{2}} ⊂ S
{{4}} ⊂ S
{4} ⊄ S
{{3}} ⊄ S
Cardinality: Cardinality of a set A is defined as the number of elements in the set A, and is written as |A|.
Set Operations:
- Union
A ∪ B = {x | x ∈ A or x ∈ B}
- Intersection
A ∪ B = {x | x ∈ A and x ∈ B}
- Difference or relative compliment
A - B = {x | x ∈ A or x ∉ B}
- Cartesian Product
A X B = {(x, y) | x ∈ A or y ∈ B}