Math Chapter one

1)      AUB

U = Union mean write in sequence which also include repeat one time.

Let’s Example two set one is A and another one is B:

A =  {1, 2,  5,  8}    B = {  1, 3, 5, 9 }

AUB = A Union B

Answer.

   AUB = { 1,  2,   5,  8 }  U   { 1,  3,  5,  9}

   AUB ={1, 2, 3, 5, 8, 9}  Ans.

Note : which show the indicate of different color actually write one this indicate means.

2)      A П B

П = intersection

Means write duplicate value two set one time.

A =  {1, 2,  5,  8}    B = {  1, 3, 5, 9 }

A П B

AUB = A intersection  B

Answer.

   A П B  = { 1,  2,   5,  8 }  U   { 1,  3,  5,  9}

   AUB ={ 1 , 5 }  Ans.

Difference Between Two Set ( A – B)

           (A – B)

         ( --) show difference between two set

    We have sample difference number it like same.

Let’s example :

 (A-B) 

 A =  {1, 2,  5,  8}    B = {  1, 3, 5, 9 }

Answer.

   A - B = { 1,  2,   5,  8 } -  { 1,  3,  5,  9}

   AUB ={ 2 ,  8 }  Ans.

Write only A  set remaining value.

3)      ( A U B) П ( A U C)

A = {a, ,b c }  B = { b, c, d, e }  C= { c, d, e, f, h }

Taking Left Hand Side First

( A U B)

( A U B ) =  { a, b, c }  U {  b, c, d, e}

(AUB) = { a,b, c, d, e}

Taking right side

(A U C)

(A U C) = { a,b, c} U { b, c, d, e}

(A U C) = {a,b,c, d , e}

( A U B) П ( A U C)  Taking 

( A U B) П ( A U C) = {  a,b, c, d, e  } П {a,b,c, d , e}

( A U B) П ( A U C) =  {  a,b, c, d, e } Ans.

              Example De Morgan’s  Law

(AUB)’ = A’ПB’

( ‘ ) show Universal number

Let’s  U {  1, 2, 3, 4, 5, 6, 7 }, A= { 1, 3 5, 7}  B = { 3,4, 5, 6}

Solutions:

i)                    Here  U = {  1,  2, 3, 4, 5 , 6 , 7  }, A = { 1, 3, 5 ,7} and  B=  { 3, 4, 5, 6 }

          

First Taking Right Hand Side

AUB = {  1, 3, 5, 7, } U { 3, 4,  5, 6}

AUB = {  1,3,4,5,6,7 }

We find now,

(AUB)’ =  U – (AUB)

U – (AUB) =  ( 1, 2, 3, 4, 5, 6, 7 ) –  ( 1, 3, 4, 5, 6, 7 )

(AUB)’ =  {  2 }  because difference both set.

U – ( AUB) =  {  2  }      =>   

Taking Left Hand Side :

A’ПB’   = >   U – A   =>  U -B

U – A = { 2,4, 6  }

A’  = >  U – A  =   { 1, 2, 3, 4, 5, 6, 7 } – { 1,  3, 5, 7 }   = > 

U- B =  { 1, 2, 7  }

B’  = >  U – B =  { 1, 2, 3, 4, 5, 6, 7   }  -  {  3, 4, 5, 6 }  =>    

A’П B’ =  {   2  } Ans.

A’ПB’    =  { 2,4, 6  }  П  { 1, 2, 7  }    = >

(AUB)’ = A’ПB’

Now you see that both value become same this means that we verify De – Morgam Rule.