Let $A = \{a, e, i, o, u\}$ and $B = \{a, i, u\}$. Show that $A \cup B = A$.
(N/A) We have $A = \{a, e, i, o, u\}$ and $B = \{a, i, u\}$.
$A \cup B = \{a, e, i, o, u\} \cup \{a, i, u\} = \{a, e, i, o, u\}$.
Since the resulting set is exactly $A$,we have $A \cup B = A$.
This example illustrates that the union of a set $A$ and its subset $B$ is the set $A$ itself,i.e.,if $B \subset A$,then $A \cup B = A$.
$A \cup B = \{a, e, i, o, u\} \cup \{a, i, u\} = \{a, e, i, o, u\}$.
Since the resulting set is exactly $A$,we have $A \cup B = A$.
This example illustrates that the union of a set $A$ and its subset $B$ is the set $A$ itself,i.e.,if $B \subset A$,then $A \cup B = A$.
Explore More
Similar Questions
Consider the sets $A$ and $B$ where $A = \{2, 4, 6, 8\}$ and $B = \{6, 8, 10, 12\}$. Find $A \cap B$.
Easy
View SolutionIf $A$ and $B$ are two sets such that $n(A) = 0.16$,$n(B) = 0.14$,and $n(A \cup B) = 0.25$,then $n(A \cap B)$ is equal to:
Easy
View SolutionIf $A = \{3, 5, 7, 9, 11\}$,$B = \{7, 9, 11, 13\}$,$C = \{11, 13, 15\}$ and $D = \{15, 17\}$; find $B \cap C$.
Easy
View SolutionShow that for any sets $A$ and $B$,$A = (A \cap B) \cup (A - B)$ and $A \cup (B - A) = (A \cup B).$
Medium
View SolutionIf sets $A$ and $B$ are defined as follows:
$A = \{(x, y) : y = \frac{1}{x}, 0 \neq x \in R\}$
$B = \{(x, y) : y = -x, x \in R\}$,then
$A = \{(x, y) : y = \frac{1}{x}, 0 \neq x \in R\}$
$B = \{(x, y) : y = -x, x \in R\}$,then
Medium
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