Write the negation of the following statement and check whether the resulting statement is true:
Every natural number is greater than $0.$
Every natural number is greater than $0.$
(N/A) The negation of the statement is:
It is false that every natural number is greater than $0.$
This can be rewritten as:
There exists a natural number which is not greater than $0.$
Since all natural numbers are defined as $n \in \{1, 2, 3, \dots\}$,every natural number is indeed greater than $0.$ Therefore,the negation statement is false.
It is false that every natural number is greater than $0.$
This can be rewritten as:
There exists a natural number which is not greater than $0.$
Since all natural numbers are defined as $n \in \{1, 2, 3, \dots\}$,every natural number is indeed greater than $0.$ Therefore,the negation statement is false.
Explore More
Similar Questions
Write the contrapositive of the following statement:
If a number is divisible by $9,$ then it is divisible by $3.$
If a number is divisible by $9,$ then it is divisible by $3.$
Easy
View SolutionLet $r \in \{p, q, \sim p, \sim q\}$ be such that the logical statement $r \vee (\sim p) \Rightarrow (p \wedge q) \vee r$ is a tautology. Then $r$ is equal to
DifficultJEE MAIN 2022
View SolutionWrite the negation of the following statement:
$\sqrt{7}$ is rational.
$\sqrt{7}$ is rational.
Easy
View SolutionThe expression $(p \wedge \sim q) \vee q \vee (\sim p \wedge q)$ is equivalent to
The negation of $p \rightarrow (\sim p \vee q)$ is
DifficultKCET 2011
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