Math, asked by sujalabhinav74, 11 months ago

let A and B be two sets then (A U B)' U(A' ∩ B) is equal to

Answers

Answered by Prahem54
27

Union means addition of all the elements of both the sets.

Intersection means common elements of both the sets.

----------------------------------------------------------------------------------------------------

Since AUB=A

It indicates B is a empty set or have same elements which set A have  because at union fuction also the answer is A.

So it it conclude that if set B is null set then 

A∩B=A

and if set B have same element that set A have then

A∩B=A or A∩B=B.

Answered by parulsehgal06
4

Answer:

The value of (AUB)'U(A'∩B) = A'

Step-by-step explanation:

De-Morgan's Law:

De - Morgan's First law:

It states that the complement of the union of two sets is the intersection of their complements.

(AUB)' = A'∩B'

De - Morgan's Second Law:

It states that the complement of the intersection of two sets is the union of their complements.

(A∩B)' = A'UB'

These two laws are called De Morgan's Law.

Let S = (AUB)'U(A'∩B)

         According to De - Morgan's law,   (AUB)' = A'∩B'

     S  = (A'∩B')U(A'∩B)

         = (A'UA')∩(A'UB)∩(B'UA')∩(B'UB)

         = A' ∩ {AU(B∩B')} ∩ U

  where U is the universal set

     S = A' ∩ (A'∪ ∅) ∩ U

        =  A' ∩ A' ∩ U

        =  A' ∩ U

    S  =  A'

     Hence (AUB)'U(A'∩B) = A'

Know more about Algebra:

https://brainly.in/question/21098904?referrer=searchResults

   

Similar questions