Which of the following statements are true and which are false? In each case give a valid reason for saying so.
$s:$ If $x$ and $y$ are integers such that $x > y,$ then $-x < -y.$
$s:$ If $x$ and $y$ are integers such that $x > y,$ then $-x < -y.$
(A) Given the inequality $x > y$.
According to the rules of inequality,if we multiply both sides of an inequality by a negative number,the direction of the inequality sign reverses.
Multiplying both sides by $-1$,we get:
$(-1) \times x < (-1) \times y$
$-x < -y$
Thus,the given statement $s$ is true.
According to the rules of inequality,if we multiply both sides of an inequality by a negative number,the direction of the inequality sign reverses.
Multiplying both sides by $-1$,we get:
$(-1) \times x < (-1) \times y$
$-x < -y$
Thus,the given statement $s$ is true.
Explore More
Similar Questions
Write the contrapositive of the following statement:
If a triangle is equilateral,it is isosceles.
If a triangle is equilateral,it is isosceles.
Easy
View SolutionWrite the following statement in the form "if $p$,then $q$":
$r$: You can access the website only if you pay a subscription fee.
$r$: You can access the website only if you pay a subscription fee.
Easy
View SolutionIf the statement $p \leftrightarrow (q \rightarrow p)$ is false,then the true statement/statement pattern is
Give three examples of sentences which are not statements. Give reasons for the answers.
Easy
View SolutionIf the truth value of the statement $p \to (\sim q \vee r)$ is false $(F)$,then the truth values of the statements $p, q, r$ are respectively:
DifficultJEE MAIN 2019
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