Given the sets $A = \{1, 3, 5\}$,$B = \{2, 4, 6\}$,and $C = \{0, 2, 4, 6, 8\}$,which of the following sets can be considered as a universal set for all the three sets $A$,$B$,and $C$?
$X = \{0, 1, 2, 3, 4, 5, 6\}$
$X = \{0, 1, 2, 3, 4, 5, 6\}$
(D) universal set for a collection of sets must contain all elements present in every set of that collection.
For the given sets $A = \{1, 3, 5\}$,$B = \{2, 4, 6\}$,and $C = \{0, 2, 4, 6, 8\}$,the universal set $U$ must satisfy $A \subseteq U$,$B \subseteq U$,and $C \subseteq U$.
Checking the set $X = \{0, 1, 2, 3, 4, 5, 6\}$:
$A \subset X$ is true.
$B \subset X$ is true.
However,$C \not\subset X$ because the element $8 \in C$ but $8 \notin X$.
Therefore,the set $\{0, 1, 2, 3, 4, 5, 6\}$ is not a universal set for $A$,$B$,and $C$.
For the given sets $A = \{1, 3, 5\}$,$B = \{2, 4, 6\}$,and $C = \{0, 2, 4, 6, 8\}$,the universal set $U$ must satisfy $A \subseteq U$,$B \subseteq U$,and $C \subseteq U$.
Checking the set $X = \{0, 1, 2, 3, 4, 5, 6\}$:
$A \subset X$ is true.
$B \subset X$ is true.
However,$C \not\subset X$ because the element $8 \in C$ but $8 \notin X$.
Therefore,the set $\{0, 1, 2, 3, 4, 5, 6\}$ is not a universal set for $A$,$B$,and $C$.
Explore More
Similar Questions
Two finite sets have $m$ and $n$ elements respectively. The total number of subsets of the first set is $56$ more than the total number of subsets of the second set. The values of $m$ and $n$,respectively are
State which of the following sets are finite or infinite:
$\{ x : x \in \mathbb{N} \text{ and } (x - 1)(x - 2) = 0 \}$
$\{ x : x \in \mathbb{N} \text{ and } (x - 1)(x - 2) = 0 \}$
Medium
View SolutionIn each of the following,determine whether the statement is true or false. If it is true,prove it. If it is false,give a counterexample.
If $A \subset B$ and $B \in C,$ then $A \in C$.
If $A \subset B$ and $B \in C,$ then $A \in C$.
Easy
View SolutionConsider the sets $\phi, A = \{1, 3\}, B = \{1, 5, 9\}, C = \{1, 3, 5, 7, 9\}$. Insert the symbol $\subset$ or $\not\subset$ between the pair of sets: $B \dots C$.
Easy
View SolutionThe number of elements in the set $\{ (a, b) : 2a^2 + 3b^2 = 35, a, b \in Z \} $,where $Z$ is the set of all integers,is
Difficult
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