Question:

Find sets A, B and C such that \(A ∩ B, B ∩ C\) and \(A ∩ C\) are non-empty sets and \(A ∩ B ∩ C = \phi.\)

Updated On: Oct 23, 2023
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Solution and Explanation

Let A = {0, 1}, B = {1, 2}, and C = {2, 0}. 
Accordingly, \(A ∩ B =\) {1}, \(B ∩ C =\) {2}, and \(A ∩ C =\) {0}. 
\(∴ A ∩ B, B ∩ C,\) and \(A ∩ C\) are non-empty. 
However, \(A ∩ B ∩ C = \phi\)

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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”