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SETS - Coggle Diagram
SETS
SET CONCEPT
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A set is a collection of well-defined objects called elements. By 'well-defined' we mean that there is some criterion that enables us to make one of the following decisions about an element that we shall designate by a
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Sets are denoted by capital letters, such as A, B, C
If the set A contains the object x, it is said that x is an element of A and it is denoted by xA
If the set A does not contain the object x, it is said that x isn't an element of A and it is denoted by xA
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REPRESENTATION OF SETS
Venn Diagram
Elements of a set are written in a simple closed shape. This type of representation is called Venn diagram
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.
Set-Builder Form
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.
OPERATION ON SETS
INTERSECTION OF SETS
The intersections of sets A and The intersection 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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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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INFINITE SETS
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For example; 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"
example; the set of all natural numbers N={0,1,2,3,4,...}
For If the elements of a set are not countable then, this set is called infinite set otherwise it is called finite set.
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 A≠B.