Find the component statements of the following compound statement and check whether they are true or false.
$100$ is divisible by $3, 11$ and $5$.
$100$ is divisible by $3, 11$ and $5$.
The component statements are as follows:
$p: 100$ is divisible by $3$.
$q: 100$ is divisible by $11$.
$r: 100$ is divisible by $5$.
Checking the truth values:
$100$ is not divisible by $3$,so $p$ is false.
$100$ is not divisible by $11$,so $q$ is false.
$100$ is divisible by $5$,so $r$ is true.
$p: 100$ is divisible by $3$.
$q: 100$ is divisible by $11$.
$r: 100$ is divisible by $5$.
Checking the truth values:
$100$ is not divisible by $3$,so $p$ is false.
$100$ is not divisible by $11$,so $q$ is false.
$100$ is divisible by $5$,so $r$ is true.
Explore More
Similar Questions
The negation of the Boolean expression $x \leftrightarrow \sim y$ is equivalent to
Show that the statement "For any real numbers $a$ and $b$,$a^{2}=b^{2}$ implies that $a=b$" is not true by giving a counter-example.
Medium
View SolutionThe logical statement $(p$ $\Rightarrow q) \wedge (q$ $\Rightarrow \sim p)$ is equivalent to
DifficultJEE MAIN 2020
View SolutionIf $p$ and $q$ each have truth value $F$,then the truth values of the statement patterns $(\sim p \vee q) \leftrightarrow \sim(p \wedge q)$ and $\sim p \leftrightarrow (p \rightarrow \sim q)$ respectively are
The statement pattern $p$ $\rightarrow (q$ $\rightarrow p)$ is equivalent to
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