COMPLEMENT OPERATIONS WITH TWO SETS

Complement is one of the important operations on sets which can be used to find the difference between the universal set and the given set. 

If X ⊆ U, where U is a universal set, then U \ X is called the compliment of X with respect to U. If underlying universal set is fixed, then we denote U \ X by X' and it is called compliment of X.

X'  =  U \ X 

The difference set set A \ B can also be viewed as the compliment of B with respect to A.  

Question 1 :

If A and B are two sets and U is the universal set such that n(U)  =  700, n(A)  =  200, n(B)  =  300 and n (A∩B) = 100, find n (A'∩B').

Solution :

n (U)  =  700

n (A)  =  200

n(B)  =  300

n (A∩B)  =  100

n (A'∩B')  =  n (AUB)'

To find n (AUB)' we have to use the formula for n (AUB)

n (AUB)  =  n(A) + n(B) - n(A∩B)

  =  200 + 300 - 100

  =  500 - 100

  =  400

n (AUB)'  =  n(U) - n (AUB)

  =  700 - 400

  =  300

n(A'∩B')  =  n(AUB)'

n (A'∩B')  =  300

Question 2 :

Given n(A) = 285, n(B) = 195, n(U) = 500, n(AUB) = 410, find n (A'UB')

Solution :

n(A)  =  285

n(B)  =  195

n(U)  =  500

n(AUB)  =  410

n(A'UB')  =  n(A∩B)'

To find n(A∩B)' first we have to find n(A∩B)

n(A∩B)  =  n(A) + n(B) - n(AUB)

  =  285+195-410

  = 480-410

  =  70

n (A∩B)'  =  n(U) - n(A∩B)

  =  500-70

n(A∩B)'  =  430

• Back to worksheet
  
• Definition
• Representation of Set 
• Types of set
• Disjoint sets 
• Power Set
  
• Operations on Sets
• Laws on set operations
• More Laws
• Venn diagrams
• Set word problems
• Relations and functions

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