Question:

State whether each of the following statement is true or false. Justify your answer.
(i) {2, 3, 4, 5} and {3, 6} are disjoint sets.
(ii) {a, e, i, o, u} and {a, b, c, d} are disjoint sets.
(iii) {2, 6, 10, 14} and {3, 7, 11, 15} are disjoint sets.
(iv) {2, 6, 10} and {3, 7, 11} are disjoint sets.

Updated On: Oct 22, 2023
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Solution and Explanation

(i) False
As 3 \(\in\) {2, 3, 4, 5}, 3 \(\in\) {3, 6}
\(⇒\) {2, 3, 4, 5} \(\cap\) {3, 6} = {3}


(ii) False
As a \(\in\) {a, e, i, o, u}, a \(\in\) {a, b, c, d}
\(⇒\) {a, e, i, o, u } \(\cap\) {a, b, c, d} = {a}


(iii) True
As {2, 6, 10, 14} \(\cap\) {3, 7, 11, 15} = \(\phi\)


(iv) True
As {2, 6, 10} \(\cap\) {3, 7, 11} = \(\phi\)

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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”