Operations on Sets

Operations on sets include intersection, union and difference of two sets.

Examples on operations on sets :

1) If A = { x | x ≤6 ; x ∈ N} and B = {x |3 ≤ x < 9, x ∈ N} ,
find i) A ∪ B (ii) A ∩ B (iii) A - B (iv) B - A.

Solution :
A = { x | x ≤6 ; x ∈ N} = { 1,2,3,4,5,6}

B = {x |3 ≤ x < 9, x ∈ N} = { 3,4,5,6,7,8}

(i) A ∪ B = { 1,2,3,4,5,6} ∪ { 3,4,5,6,7,8}

= { 1,2,3,4,5,6,7,8}.

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

= {3,4,5,6}.

(iii) A - B = { 1,2,3,4,5,6} - { 3,4,5,6,7,8}

= {1,2}

(iv) B - A = { 3,4,5,6,7,8} - { 1,2,3,4,5,6}

= { 7,8}

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2) If U = ξ = {x |x ≤ 8, x ∈ W}, A = { x|2x -1 ≤ 8; x ∈ W}and
B = { x|5x -1 ≤ 14, x ∈ N}. Find (i) (A ∪ B)' (ii) A' ∩ B'

Solution :
U = ξ = {x |x ≤ 8, x ∈ W} = {0,1,2,3,4,5,6,7,8}

A = { x|2x -1 ≤ 8; x ∈ W}= { x|x ≤ 9/2; x ∈ W} = {0,1,2,3,4}

B = { x|5x -1 ≤ 14, x ∈ N}= {x|x ≤ 3, x ∈ N} ={1,2,3}

(i) (A ∪ B)= {0,1,2,3,4} ∪ {1,2,3}= {0,1,2,3,4}

∴ (A ∪ B)' = {5,6,7,8}

(ii) A' = {5,6,7,8} and B' = {0,4,5,6,7,8}

∴ A' ∩ B'= {5,6,7,8}

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3) If A ={ 6,7,8,9,10,11,12,13,14} , B= { 11,12,13,14,15,16,17,18,19} and
C = {16,17,18,19,20,21,22,23,24}. Find A ∪ ( B ∩ C)

Solution:
First we will find B ∩ C

B ∩ C = { 11,12,13,14,15,16,17,18,19} ∩ {16,17,18,19,20,21,22,23,24}

B ∩ C = { 16,17,18,19}

Now, A ∪ ( B ∩ C) = { 6,7,8,9,10,11,12,13,14} ∪ { 16,17,18,19}

A ∪ ( B ∩ C) = {6,7,8,9,10,11,12,13,14, 16,17,18,19}

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Set Theory

• Sets
• Representation of Set
• Cardinal Number
• Types of Sets
• Pairs of Sets
• Subset
• Complement of Set
• Union of the Sets
• Intersection of Sets
• Operations on Sets
• De Morgan's Law
• Venn Diagrams
• Venn-diagrams for sets
• Venn-diagrams for different situations
• Problems on Intersection of Two Sets
• Problems on Intersection of Three Sets
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