Sets

Maths Project SETS Submitted To : Joseph Sir

Set and its notation ,[object Object],[object Object],[object Object],[object Object],[object Object],. Introduction : A set is an unordered collection of elements. Examples. Note:   {  }

Subsets ,[object Object],[object Object],[object Object],or, “ B contains A .” or, “every element of A is also in B .” or,  x (( x  A )  ( x  B )). Venn Diagram B A

Superset ,[object Object],[object Object],[object Object],iff, A  B and B  A iff, A  B and A  B iff,  x (( x  A )  ( x  B )). ,[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],A B

Power sets ,[object Object],[object Object],If S = { a } If S = { a,b } If S =  If S = {  ,{  }} We say, “ P ( S ) is the set of all subsets of S .” 2 S = {  , { a }}. 2 S = {  , {a}, {b}, {a,b}}. 2 S = {  }. 2 S = {  , {  }, {{  }}, {  ,{  }}}.

Union ,[object Object],[object Object],If A = {Charlie, Lucy, Linus}, and B = {Lucy, Desi}, then A  B = {Charlie, Lucy, Linus, Desi} A B

Intersection ,[object Object],[object Object],If A = {Charlie, Lucy, Linus}, and B = {Lucy, Desi}, then A  B = {Lucy} A B

Complement ,[object Object],If A = { x : x is not shaded}, then ,[object Object],[object Object],A U

Difference ,[object Object],[object Object],= ( A – B )  ( B – A ) = { x : x  A  x  B } U A – B B – A

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Some Properties of Complement Sets 1. Complement Laws: A U A’= U A ∩ A’=  2. De Morgan’s Law: (A U B)’ = A’ ∩ B’ (A ∩ B )’ = A’ U B’ 3. Law of Double Complementation: ( A’ )’ = A 4. Laws of Empty Set and Universal Set:  ’ = U U’ = 

THANK YOU Done By : Sukesh XI- B

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