State the converse and contrapositive of the following statement:
$p:$ $A$ positive integer is prime only if it has no divisors other than $1$ and itself.
$p:$ $A$ positive integer is prime only if it has no divisors other than $1$ and itself.
(N/A) The statement $p$ can be written in the form 'If $q$,then $r$':
If a positive integer is prime,then it has no divisors other than $1$ and itself.
The converse of the statement is:
If a positive integer has no divisors other than $1$ and itself,then it is prime.
The contrapositive of the statement is:
If a positive integer has divisors other than $1$ and itself,then it is not prime.
If a positive integer is prime,then it has no divisors other than $1$ and itself.
The converse of the statement is:
If a positive integer has no divisors other than $1$ and itself,then it is prime.
The contrapositive of the statement is:
If a positive integer has divisors other than $1$ and itself,then it is not prime.
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The contrapositive of the statement 'If Jaipur is the capital of Rajasthan,then Jaipur is in India' is:
Let $\Delta, \nabla \in \{\wedge, \vee\}$ be such that $( p \rightarrow q ) \Delta ( p \nabla q )$ is a tautology. Then
DifficultJEE MAIN 2023
View SolutionWhich of the following Boolean expressions is a tautology?
The negation of $(p \wedge (\sim q)) \vee (\sim p)$ is equivalent to:
$(p \wedge r) \Leftrightarrow (p \wedge (\sim q))$ is equivalent to $(\sim p)$ when $r$ is.
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