State whether the following statement is true or false. Justify your answer.
${2, 3, 4, 5}$ and ${3, 6}$ are disjoint sets.
${2, 3, 4, 5}$ and ${3, 6}$ are disjoint sets.
(B) False.
Two sets are disjoint if their intersection is the empty set,i.e.,$A \cap B = \emptyset$.
Given sets are $A = \{2, 3, 4, 5\}$ and $B = \{3, 6\}$.
Since $3 \in A$ and $3 \in B$,the intersection is $A \cap B = \{3\}$.
Since $A \cap B \neq \emptyset$,the sets are not disjoint.
Two sets are disjoint if their intersection is the empty set,i.e.,$A \cap B = \emptyset$.
Given sets are $A = \{2, 3, 4, 5\}$ and $B = \{3, 6\}$.
Since $3 \in A$ and $3 \in B$,the intersection is $A \cap B = \{3\}$.
Since $A \cap B \neq \emptyset$,the sets are not disjoint.
Explore More
Similar Questions
If $A = \{ x : x \text{ is a natural number} \}$,$B = \{ x : x \text{ is an even natural number} \}$,$C = \{ x : x \text{ is an odd natural number} \}$,and $D = \{ x : x \text{ is a prime number} \}$,find $A \cap C$.
Easy
View SolutionIf $A = \{ x : x \text{ is a natural number} \}$,$B = \{ x : x \text{ is an even natural number} \}$,$C = \{ x : x \text{ is an odd natural number} \}$,and $D = \{ x : x \text{ is a prime number} \}$,find $B \cap D$.
Easy
View SolutionLet $A$ and $B$ be subsets of a set $X$. Then,
Easy
View SolutionIf $A = \{x : x \text{ is a multiple of } 4\}$ and $B = \{x : x \text{ is a multiple of } 6\}$,then $A \cap B$ consists of all multiples of:
Medium
View SolutionIf $A=\{3, 5, 7, 9, 11\}, B=\{7, 9, 11, 13\}, C=\{11, 13, 15\}$ and $D=\{15, 17\}$,find $A \cap (B \cup C)$.
Easy
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo