Identify the type of "Or" used in the following statement and check whether the statement is true or false:
"$A$ rectangle is a quadrilateral or a $5$-sided polygon."
"$A$ rectangle is a quadrilateral or a $5$-sided polygon."
(N/A) The statement is composed of two component statements:
$p$: $A$ rectangle is a quadrilateral.
$q$: $A$ rectangle is a $5$-sided polygon.
Here,the "Or" used is exclusive because a rectangle cannot be both a quadrilateral and a $5$-sided polygon simultaneously.
Since $p$ is true and $q$ is false,the disjunction $p \lor q$ is true.
$p$: $A$ rectangle is a quadrilateral.
$q$: $A$ rectangle is a $5$-sided polygon.
Here,the "Or" used is exclusive because a rectangle cannot be both a quadrilateral and a $5$-sided polygon simultaneously.
Since $p$ is true and $q$ is false,the disjunction $p \lor q$ is true.
Explore More
Similar Questions
Let $A, B, C$ and $D$ be four non-empty sets. The contrapositive statement of "If $A \subseteq B$ and $B \subseteq D,$ then $A \subseteq C$" is
DifficultJEE MAIN 2020
View SolutionGiven below are two pairs of statements. Combine these two statements using "if and only if".
$p:$ If a rectangle is a square,then all its four sides are equal.
$q:$ If all the four sides of a rectangle are equal,then the rectangle is a square.
$p:$ If a rectangle is a square,then all its four sides are equal.
$q:$ If all the four sides of a rectangle are equal,then the rectangle is a square.
Easy
View SolutionWhich of the following statements is a tautology?
Difficult
View SolutionUsing the words "necessary and sufficient",rewrite the statement "The integer $n$ is odd if and only if $n^{2}$ is odd". Also,check whether the statement is true.
Easy
View SolutionWrite the following statement in the form "if $p$,then $q$":
$p$: It is necessary to have a password to log on to the server.
$p$: It is necessary to have a password to log on to the server.
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