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
Which of the following statements has the truth value $T$?
$A$: Cube roots of unity are in Geometric Progression and their sum is $0$.
$B$: $4+7 > 10$ iff $2+8 < 10$.
$C$: $\exists x \in N$ such that $x^2-3x+2=0$ and $\exists n \in N$ such that $n$ is an odd number.
$D$: $3+i$ is a complex number or $\sqrt{2}+\sqrt{3}=\sqrt{5}$.
$A$: Cube roots of unity are in Geometric Progression and their sum is $0$.
$B$: $4+7 > 10$ iff $2+8 < 10$.
$C$: $\exists x \in N$ such that $x^2-3x+2=0$ and $\exists n \in N$ such that $n$ is an odd number.
$D$: $3+i$ is a complex number or $\sqrt{2}+\sqrt{3}=\sqrt{5}$.
$(p \wedge q) \vee \sim p$ is equivalent to
$\sim (p \Rightarrow q) \Leftrightarrow \sim p \vee \sim q$ is
Medium
View SolutionWhich of the following logical equivalences is true?
Difficult
View SolutionThe negation of the proposition "If $2$ is prime,then $3$ is odd" is:
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