Set Example(1) and Tricks

1. let  A is a set such that A={a,b}

 The power set of A is P(A): is defined as a  set that contains all the subset of set A and we already know that  subsets of a set are also a set, that's why we also write-subset in set form

So subsets of A = {Ø , {a} ,{b} ,{a,b} }

P(A) ={ Ø , {a} ,{b} ,{a,b} }

P (P(A)) = { Ø ,   {Ø}   ,  {{a}}    ,    {{b}}   ,   {{a,b}}   ,   {Ø ,{a}}  ,  {Ø, {b}}   ,    {Ø ,{a,b}}   ,   {{a}, {b}}  ,    {{a} ,{a,b}}   ,   {{b}, {a,b}}   ,     {{Ø }, {a} ,{b}} ,    {{Ø } , {b} ,{a,b}}   ,   

  {{Ø } ,{a} , {a,b}}    ,     {{a} ,{b} ,{a,b}}   }

If a set  'A'contain n elements then power set  P(A ) conatain 2 elements.

 

2. Some tricks to solve questions directly.

  • A ∩ B=   AB
  • A∪ B=    A+B
  • A-B =     A ∩ B'
  • A+ AB  = A(1+B) = A      //  1+ anything =1
  • A.A'= 0
  • A+A' = 1

Disjoint Set:  Two set A and B are said to be  disjoint if A ∩ B = Ø

 

 

 

 

 

Answer
1Comment
saptarshi sahoo @saptarshi
31 Mar 2020 09:55 am
Thank you Sir, please add one more element in P (P(A))

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