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SETS - Coggle Diagram
SETS
SUBSETS
If every element of a set A is an element of set B, then A is a set to be a subset of B shown by A⊆ B.
Proper subset: If a subset of a set is not equal to itself, it is called the proper subset. If A is a proper subset of the set B, then
A⊂B or B⊃A is used to show it.
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PROPERTIES OF SUBSETS
a) Every set is a subset of universal set , that is for any set A , A .....U.
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NUMBER OF SUBSETS
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b) Any subset of a set except itself is called the proper subset of a set.
The number of proper subsets of the set A is 2n(A) – 1 = 2k – 1
GENERAL CONCEPTS IN SETS
DEFİNATION OF SETS
A set is a well-defined list of objects.
Sets are usually denoted by capital letters such as A, B, and C.
REPRESENTATİON OF SETS
Elements of a set are written in a simple closed shape. This type of representation is called Venn
diagram.
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Sometimes Venn diagram and listed form are not practical to show a set, for example the set of all
real numbers cannot be shown as a listed form or Venn diagram.
If there are some common
properties among the elements of the set, then set-builder form can be used to write it.
Example: A = {x : 2< x < 20,x N }
1.Listed form
Elements of sets are written inside of the set brackets { } by putting comma between two elements.In this form, each element is written only once and also in the set brackets the order of elements isn’t important.
Example:
A = {Positive factors of 24}
B = { Positive integers less than 14 }
C = { 1,2,3,4 }
UNIVERSAL SET (U)
The set that contains all the elements being discussed is called universal set, and it is denoted by U.
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FINITE -INFINITE SETS
A set with a natural number of elements is called a finite set. The non-finite set is called the infinite set..
For Exampl: the set A = {1, 3, 5, 7, 9, 11} is a finite set with six elements
A set that is not finite is called “infinite set”
OPERATIONS ON SETS
INTERSECTION OF SETS
The intersection of sets A and B is the set of elements which
are common for A and B,that is, those elements which belong to A and which also belong to B.
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UNION OF SETS
In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection. It is one of the fundamental operations through which sets can be combined and related to each other.
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DIFFERENCE OF TWO SETS
The difference of the sets A and B is the set of elements of A which does not belong to B, and it is
denoted by A−B or A\B.
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COMPLEMENT OF A SET
The set of all elements of the universal set that are not in A or the difference between universal set
U and the set A is called complement of A and denoted by A or A
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EQUAL SETS
Two sets contain the same elements is said to be equal sets. If A and B are equal sets, then
it is denoted by A=B; if A and B are not equal sets, they are denoted by .
DE MORGAN LAW
In propositional logic and Boolean algebra, De Morgan's laws are a pair of transformation rules that are both valid rules of inference. ... The rules allow the expression of conjunctions and disjunctions purely in terms of each other via negation.
