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Questions  >>  CBSE XI  >>  Math  >>  Mathematical Reasoning
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Write the converse and contra positive statements of the statement "You cannot comprehend geometry if you do not know how to reason deductively."

$\begin{array}{1 1} \text{Converse: If you cannot comprehend geometry you do not know how to reason deductively. contra positive: If you can comprehend geometry you know to reason deductively.} \\ \text{Converse: If you cannot comprehend geometry you know how to reason deductively. contra positive: If you cannot comprehend geometry you know to reason deductively.} \\\text{Converse: If you can comprehend geometry you do not know how to reason deductively. contra positive: If you can comprehend geometry you do not know to reason deductively.} \\ \text{Contra positive: If you cannot comprehend geometry you do not know how to reason deductively. converse: If you can comprehend geometry you know to reason deductively.}\end{array} $

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A)
Toolbox:
  • The converse of If $p$ then $q$ is If $q$ then $p$
  • The contra positive of If $p$ then $q$ is If ~$q$ then ~$p$.
The given statement is:
You cannot comprehend geometry if you do not know how to reason deductively.
The given statement can be written as
If you do no know how to reason deductively you cannot comprehend geometry.
Here $p\rightarrow$ You do not know how to reason
$q\rightarrow$ You cannot comprehend geometry.
~$p\rightarrow$ You know how to reason deductively.
~$q\rightarrow$ You can comprehend geometry.
The converse of the given statement is:
If you cannot comprehend geometry you do not know how to reason deductively.
The contra positive statement is:
If you can comprehend geometry you know to reason deductively.
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