Answer
After performing the specified steps on $p→q$ we get
converse of its inverse
$¬p$ $\rightarrow$ $¬q$
The converse of its converse
$q→p$
The converse of its contrapositive
$¬q→¬p$
Work Step by Step
the converse of its inverse
By the definitions, we know that the inverse of $p→q$ is:
$¬p→¬q$
The converse interchanges the compound propositions in the conditional statements:
$¬q→¬p$
Note: the Converse of the inverse is the contrapositive.
The converse of its converse
By the definitions, we know that the Converse of $p→q$ is:
$q→p$
the converse interchanges the compound proposition in the conditional statements:
$p→q$
Note: the Converse of the converse results in the original conditional statement.
The converse of its contrapositive
By the definition, we know that the Contrapositive of $p→q$ is
$¬q→¬p$
The converse interchanges the compound propositions in the conditional statements:
Note: The Converse of the contrapositive is the inverse.
