State whether the following statement is true or false. Justify your answer.
${2, 6, 10, 14}$ and ${3, 7, 11, 15}$ are disjoint sets.
${2, 6, 10, 14}$ and ${3, 7, 11, 15}$ are disjoint sets.
(A) The statement is $True$.
Two sets are said to be disjoint if their intersection is the empty set,denoted by $\varnothing$.
Let $A = \{2, 6, 10, 14\}$ and $B = \{3, 7, 11, 15\}$.
The intersection of $A$ and $B$ is $A \cap B = \{2, 6, 10, 14\} \cap \{3, 7, 11, 15\} = \varnothing$.
Since the intersection is empty,the sets are disjoint.
Two sets are said to be disjoint if their intersection is the empty set,denoted by $\varnothing$.
Let $A = \{2, 6, 10, 14\}$ and $B = \{3, 7, 11, 15\}$.
The intersection of $A$ and $B$ is $A \cap B = \{2, 6, 10, 14\} \cap \{3, 7, 11, 15\} = \varnothing$.
Since the intersection is empty,the sets are disjoint.
Explore More
Similar Questions
If $A = \{3, 5, 7, 9, 11\}$,$B = \{7, 9, 11, 13\}$,$C = \{11, 13, 15\}$,and $D = \{15, 17\}$,find $A \cap C \cap D$.
Easy
View SolutionIf $A = \{3, 6, 9, 12, 15, 18, 21\}$,$B = \{4, 8, 12, 16, 20\}$,$C = \{2, 4, 6, 8, 10, 12, 14, 16\}$,and $D = \{5, 10, 15, 20\}$,find $B - C$.
Easy
View SolutionIf sets $A$ and $B$ are defined as follows:
$A = \{ (x, y) : y = e^x, x \in R \}$
$B = \{ (x, y) : y = x, x \in R \}$
Then:
$A = \{ (x, y) : y = e^x, x \in R \}$
$B = \{ (x, y) : y = x, x \in R \}$
Then:
Medium
View SolutionIf $A = \{3, 5, 7, 9, 11\}$,$B = \{7, 9, 11, 13\}$,$C = \{11, 13, 15\}$,and $D = \{15, 17\}$,find $B \cap D$.
Easy
View SolutionIf $A = \{x \mid x \in N, x \text{ is a prime number less than } 12\}$ and $B = \{x \mid x \in N, x \text{ is a factor of } 10\},$ then $A \cap B = \dots$
Vedclass 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