Write the contrapositive and converse of the following statement:
If $x$ is a prime number,then $x$ is odd.
If $x$ is a prime number,then $x$ is odd.
(N/A) The given statement is of the form $P \implies Q$,where $P$ is '$x$ is a prime number' and $Q$ is '$x$ is odd'.
The contrapositive of $P \implies Q$ is $\neg Q \implies \neg P$.
Thus,the contrapositive is: If $x$ is not odd,then $x$ is not a prime number.
The converse of $P \implies Q$ is $Q \implies P$.
Thus,the converse is: If $x$ is odd,then $x$ is a prime number.
The contrapositive of $P \implies Q$ is $\neg Q \implies \neg P$.
Thus,the contrapositive is: If $x$ is not odd,then $x$ is not a prime number.
The converse of $P \implies Q$ is $Q \implies P$.
Thus,the converse is: If $x$ is odd,then $x$ is a prime number.
Explore More
Similar Questions
$(p \wedge \sim q \wedge \sim r) \vee (\sim p \wedge q \wedge \sim r) \vee (\sim p \wedge \sim q \wedge r)$ is equivalent to-
The negation of the expression $q \vee ((\sim q) \wedge p)$ is equivalent to
DifficultJEE MAIN 2023
View SolutionIf the statement pattern $(p \wedge q) \rightarrow (r \vee \sim s)$ is false,then the truth values of $p, q, r$ and $s$ are respectively:
Show that the statement $p:$ 'If $x$ is a real number such that $x^{3}+4x=0$,then $x$ is $0$' is true by the method of contradiction.
Medium
View SolutionWhat is the identity element for the conjunction $(AND)$ operation in Boolean algebra of logical statements?
Medium
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