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Have an attention plz^_^
Can anyone tell me the short summary of chapter " Sets"
mainly about vein diagrams.
"Class 11th peoples only"
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Answers
heya. .
here is you answer..
What is set ?
A set is a collection of distinct objects, considered as an object in its own right.
Venn Diagrams
●A Venn diagram is a diagrammatic representation of ALL the possible relationships between different sets of a finite number of elements. Venn diagrams were conceived around 1880 by John Venn, an English logician, and philosopher. They are extensively used to teach Set Theory.
●A Venn diagram is also known as a Primary diagram, Set diagram or Logic diagram.
Venn Diagrams
Representation of Sets in a Venn Diagram
It is done as per the following:
●Each individual set is represented mostly by a circle and enclosed within a quadrilateral (the quadrilateral represents the finiteness of the Venn diagram as well as the Universal set.)
●Labelling is done for each set with the set’s name to indicate difference and the respective constituting elements of each set are written within the circles.
●Sets having no element in common are represented separately while those having some of the elements common within them are shown with overlapping.
●The elements are written within the circle representing the set containing them and the common elements are written in the parts of circles that are overlapped.
It may help you..☺☺
↪Notes on Sets↩
● Set: A set is a well-defined collection of objects.
Representaiton of sets:
(i) Roster or Tabular form,
(ii) Rule method or set builder form.
Types of sets:
● Empty set: A set which does not contain any element is called empty set or null set or void set. It is denoted by or { }.
● Singleton set: A set, consisting of a single element, is called a singleton set.
● Finite set: A set which consists of a definite number of elements is called finite set.
● Infinite set: A set, which is not finite, is called infinite set.
● Equivalent sets: Two finite sets A and B are equivalent, if their cardinal numbers are same, .i.e, .
● Equal sets: Two sets A and B are said to be equal if they have exactly the same elements.
● Subset: A set A is said to be subset of a set B, if every element of A is also an element of B. Intervals are subsets of R.
Proper set: If A B and A B, then A is called a proper set of B, written as A B.
Universal set: If all the sets under consideration are subsets of a large set U, then U is known as a universal set. And it is denoted by rectangle in Venn-Diagram.
Power set: A power set of a set A is collection of all subsets of A. It is denoted by P(A).
● Venn-Diagram: A gepmetrical figure illustrating universal set, subsets and their operations is known as Venn-Diagram.
● The union of two sets A and B is the set of all those elements which are either in A or in B.
● Intersection of sets: The intersection of two sets A and B is the set of all elements which are common. The difference of two sets A and B in this order is the set of elements which belong to A but not to B.
● Disjoint sets: Two sets A and B are said to be disjoint, if .
Difference of sets: Difference of two sets i.e., set (A – B) is the set of those elements of A which do not belong to B.
● Compliment of a set: The complement of a subset A of universal set U is the set of all elements of U which are not the elements of A. A’ = U – A.
For any two sets A and B, (A ∪ B)′ = A′ ∩ B′ and ( A ∩ B )′ = A′ ∪ B′
If A and B are finite sets such that A ∩ B = φ, then
n (A ∪ B) = n (A) + n (B).
If A ∩ B ≠ φ, then
n (A ∪ B) = n (A) + n (B) – n (A ∩ B)