PRACTICE PROBLEMS ON UNION INTERSECTION AND COMPLEMENT

Question 1 :

If A ⊂ B,then show that A U B = B (use venn diagram)

Solution :

Since A is the subset of B we have to draw a small circle A inside the large circle B.

A U B = B

Question 2 :

If A ⊂ B, then find A∩B and A\B (use venn diagram)

Solution :

Since A is the subset of B we have to draw a small circle A inside the large circle B.

A∩B means we have to shade common part of A and B. From this we will get 

A∩B  =  A

Question 3 :

Let P  =  {a, b, c}, Q  =  {g, h, x, y} and R  =  {a, e, f, s}. Find the following

(i) P\R        (ii)  Q∩R        (iii) R\(P∩Q)

Solution :

(i) To find P\R we have to choose the common elements from both P and R and we have to write remaining elements in P.

P\R  =  {a, b, c} \ {a, e, f, s}

  =  {b, c}

(ii) To find Q∩R we have to write the common elements in Q and R.

Q∩R   =  {g, h, x, y} ∩ {a, e, f, s}

there is no common elements in both Q and R

Q∩R   =  Ø

(iii) R\(P∩Q)

P∩Q  =  {a, b, c} ∩ {g, h, x, y}

There is no common elements in both P and Q

P∩Q  =  Ø

R\(P∩Q)  =  {a, b, c}\Ø

  =  {a,b,c}     

Question 4 :

If A  =  4, 6, 7, 8, 9} , B  =  {2, 4, 6} and C  =  {1, 2, 3, 4, 5, 6}, then find

(i) AU(B∩C)    (ii) A∩(BUC)       (iii) A\(C\B)

Solution :

(i) AU(B∩C)

(B∩C)  =  {2, 4, 6} ∩ {1, 2, 3, 4, 5, 6}

  =  {2, 4, 6}

AU(B∩C)  =  {4, 6, 7, 8, 9} U {2, 4, 6}

  =  {2, 4, 6, 7, 8, 9}

(ii) A∩(BUC)

(BUC)  =  {2, 4, 6} U {1, 2, 3, 4, 5, 6}

=  {1, 2, 3, 4, 5, 6}

A∩(BUC)  =  {4, 6, 7, 8, 9} ∩ {1, 2, 3, 4, 5, 6}

   =  {4, 6}

(iii) A\(C\B)

C\B  =  {1, 2, 3, 4, 5, 6}\{2, 4, 6}

  =  {1, 3, 5}

A\(C\B)  =  {4, 6, 7, 8, 9}\{1, 3, 5}

  =  {4, 6, 7, 8, 9}

Related topics

• 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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