Operations on Sets

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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}

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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