Question:

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find
(i) \(A∪ B\)
(ii) \(A ∪ C\)
(iii) \(B ∪ C\)
(iv) \(B ∪ D\)
(v) \(A ∪ B ∪ C\)
(vi) \(A∪ B ∪ D\)
(vii) \(B ∪ C ∪ D\)

Updated On: Oct 22, 2023
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Solution and Explanation

A = {1, 2, 3, 4], B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}

(i) \(A ∪ B\) = {1, 2, 3, 4, 5, 6}


(ii) \(A ∪ C\) = {1, 2, 3, 4, 5, 6, 7, 8}


(iii) \(B ∪ C \)= {3, 4, 5, 6, 7, 8}


(iv) \(B∪ D \)= {3, 4, 5, 6, 7, 8, 9, 10}


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


(vi) A ∪ B ∪ D = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}


(vii) B ∪ C ∪ D = {3, 4, 5, 6, 7, 8, 9, 10}

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Concepts Used:

Operations on Sets

Some important operations on sets include union, intersection, difference, and the complement of a set, a brief explanation of operations on sets is as follows:

1. Union of Sets:

  • The union of sets lists the elements in set A and set B or the elements in both set A and set B.
  • For example, {3,4} ∪ {1, 4} = {1, 3, 4}
  • It is denoted as “A U B”

2. Intersection of Sets:

  • Intersection of sets lists the common elements in set A and B.
  • For example, {3,4} ∪ {1, 4} = {4}
  • It is denoted as “A ∩ B”

3.Set Difference:

  • Set difference is the list of elements in set A which is not present in set B
  • For example, {3,4} - {1, 4} = {3}
  • It is denoted as “A - B”

4.Set Complement:

  • The set complement is the list of all elements present in the Universal set except the elements present in set A
  • It is denoted as “U-A”