Write the contrapositive and converse of the following statement:
"You cannot comprehend geometry if you do not know how to reason deductively."
"You cannot comprehend geometry if you do not know how to reason deductively."
(N/A) The given statement is of the form "If $p$,then $q$",where $p$ is "You do not know how to reason deductively" and $q$ is "You cannot comprehend geometry".
The contrapositive of "If $p$,then $q$" is "If not $q$,then not $p$".
Here,not $q$ is "You can comprehend geometry" and not $p$ is "You know how to reason deductively".
Thus,the contrapositive is: "If you can comprehend geometry,then you know how to reason deductively."
The converse of "If $p$,then $q$" is "If $q$,then $p$".
Thus,the converse is: "If you cannot comprehend geometry,then you do not know how to reason deductively."
The contrapositive of "If $p$,then $q$" is "If not $q$,then not $p$".
Here,not $q$ is "You can comprehend geometry" and not $p$ is "You know how to reason deductively".
Thus,the contrapositive is: "If you can comprehend geometry,then you know how to reason deductively."
The converse of "If $p$,then $q$" is "If $q$,then $p$".
Thus,the converse is: "If you cannot comprehend geometry,then you do not know how to reason deductively."
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