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SETTS - Coggle Diagram
SETTS
Definiation:Set is a mathematically undefined concept. This concept is interpreted as a "collection or stack of objects". The "object" in this definition is something abstract or concrete. ... So, in mathematics, "A collection of well-defined objects is called a set.
Empty Set
An empty set is a set that has no elements in mathematics.
It shows like this Ø {}
eg:Set A, months beginning with the letter "C".
This is a empty set A {}
SUBSET
In mathematical science, A and B are considered as two separate sets.If every element of set A also belongs to set B, set A is called a subset of set B. The set B is also called the set that includes the set A.
A={bookshelf,clock,table,mirror,bed} s(A)=5 The number of elements is 5.
A set whose number of elements can be expressed as a natural number is called a finite set.
Sets with the same number of elements are called equivalent sets.
D={1,2,3,4} s(D)=4
C={a,b,c,d} s(C)=4
Then we say C≡D.
Number of Subsets
The number of subsets of a set with n elements is found with the formula 2n.
Subsets of a set excluding itself are called self-subsets. It is found with the formula 2n-1.
Example: A ={a,b,{b,c},c,{b},{a,c}}
Number of elements of the set s(A)=6
Number of subsets of the set 2n=26=64
The number of self-subsets of the set is 2n-1=26-1=64-1=63
symbols that we use:
{ } set a collection of elements A = {1, 7, 9, 13, 15, 23},
B = {7, 13, 15, 21}
A ∪ B union Elements that belong to set A or set B A ∪ B = {1, 7, 9, 13, 15, 21, 23}
A ∩ B intersection Elements that belong to both the sets, A and B A ∩ B = {7, 13, 15 }
A ⊆ B subset subset has few or all elements equal to the set {7, 15} ⊆ {7, 13, 15, 21}
A ⊄ B not subset left set is not a subset of right set {1, 23} ⊄ B
A ⊂ B proper subset / strict subset subset has fewer elements than the set {7, 13, 15} ⊂ {1, 7, 9, 13, 15, 23}
A ⊃ B proper superset / strict superset set A has more elements than set B {1, 7, 9, 13, 15, 23} ⊃ {7, 13, 15, }
