SET OPERATIONS

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SET OPERATIONS : 

SET OPERATIONS By Pradeep Kumar Pradnya Mazagaonkar Preeti Gusain Priyanka Rai Ramendra Yadav

What Is A Set? : 

What Is A Set? Set- A collection of well defined objects. Usually denoted by Capital letters. Elements – Objects that form a set. x ϵ S meaning ‘x belongs to S’ Representation of a set – A = {2, 3, 5, 7,} B = {x | x is a prime number; x < 10}

Types Of Sets : 

Types Of Sets Singleton Set C = {7} Empty Set D = { } or φ Equal Sets A = {2, 3} B = {2, 3} A = B Universal Set

Types Of Sets (Contd…) : 

Types Of Sets (Contd…) Subset If every element of set A is also an element of set B, then A is a subset of B. A = {2,5} B = {1, 2, 3, 5, 7} Every set is a subset of itself. Compliment of a set X A’ A

Operations On Sets : 

Operations On Sets Union Of Sets If A and B are two subsets of Universal Set X, then the set of those elements which belong to A or to B or to both A and B, is called the union of the sets A and B and is denoted by A U B X A B

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2. Intersection Of Sets If A and B are two subsets of Universal Set X, then the set of those elements which belong to both A and B, i.e., which are common to both A and B, is called the intersection of the sets A and B and is denoted by A B X A B

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3. Disjoint Sets Disjoint sets have no element in common, i.e., their intersection set does not contain any element. Hence A B = φ X A B

Properties Of Union and Intersection : 

Properties Of Union and Intersection Properties Of Union 1. A U B = B U A 2. A U (B U C) = (A U B) U C 3. A U A = A 4. A U φ = A 5. A U X = X 6. A U A’ = X

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Properties Of Intersection 1. A B = B A 2. A (B C) = (A B) C 3. A A = A 4. A φ = φ 5. A X = A 6. A A’ = φ

De Morgan’s Laws : 

De Morgan’s Laws (A U B)’ = A’ B’ 2. (A B)’ = A’ U B’ X A B X A B

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THANK YOU

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