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Home  >>  CBSE XI  >>  Math  >>  Mathematical Reasoning
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For the statement "If you live in Delhi then you have winter clothes.' is the statement "If you do not have winter clothes then you do not live in Delhi" contra positive or converse?

$\begin{array}{1 1} Contra\;positive \\ converse \end{array} $

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Toolbox:
  • The contra positive of ' If $p$ then $q$ is If ~$q$ then ~$p$
  • The converse of ' If $p$ then $q$ is If $q$ then $p$
The given statements are
1. "If you live in Delhi then you have winter clothes".
2. "If you do not have winter clothes then you do not live in Delhi"
Here the second statement is contra positive of first one.
Because for first statement,
$p\rightarrow$ You live in Delhi.
$q\rightarrow$ You have winter clothes.
~$p\rightarrow$ You do not live in Delhi.
~$q\rightarrow$ You do not have winter clothes..
The contra positive of ' If $p$ then $q$ is If ~$q$ then ~$p$
answered Jul 22, 2014 by rvidyagovindarajan_1
edited Jul 22, 2014 by rvidyagovindarajan_1
 

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