In 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 $x \in A$ and $A \not\subset B$,then $x \in B$
If $x \in A$ and $A \not\subset B$,then $x \in B$
(N/A) The statement is $False$.
To disprove the statement,we provide a counterexample.
Let $A = \{1, 2\}$ and $B = \{1, 3\}$.
Here,$A \not\subset B$ because $2 \in A$ but $2 \notin B$.
Let $x = 2$. Then $x \in A$ and $A \not\subset B$ are satisfied.
However,$x \notin B$ because $2 \notin \{1, 3\}$.
Thus,the statement is $False$.
To disprove the statement,we provide a counterexample.
Let $A = \{1, 2\}$ and $B = \{1, 3\}$.
Here,$A \not\subset B$ because $2 \in A$ but $2 \notin B$.
Let $x = 2$. Then $x \in A$ and $A \not\subset B$ are satisfied.
However,$x \notin B$ because $2 \notin \{1, 3\}$.
Thus,the statement is $False$.
Explore More
Similar Questions
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 $C$?
$X = \{0, 1, 2, 3, 4, 5, 6\}$
$X = \{0, 1, 2, 3, 4, 5, 6\}$
Easy
View SolutionIf $aN = \{ ax : x \in N \}$,then the set $3N \cap 7N$ is .....$N$.
Medium
View SolutionExamine whether the following statement is true or false:
${1, 2, 3} \subset {1, 3, 5}$
${1, 2, 3} \subset {1, 3, 5}$
Easy
View SolutionWhich of the following pairs of sets are equal? Justify your answer.
$X$,the set of letters in "$ALLOY$" and $B$,the set of letters in "$LOYAL$".
$X$,the set of letters in "$ALLOY$" and $B$,the set of letters in "$LOYAL$".
Medium
View SolutionDetermine whether the following set is finite or infinite:
The set of positive integers greater than $100$.
The set of positive integers greater than $100$.
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