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Questions  >>  CBSE XI  >>  Math  >>  Mathematical Reasoning
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Q)

Write the converse and contra positive statements of the statement "Something cold implies that it has low temperature."

$\begin{array}{1 1} \text{Converse: If something is at low temperature then it is not cold. and contra positive: If something is not at low temperature then it is not cold.} \\ \text{Converse: If something is at low temperature then it is cold. and contra positive: If something is not at low temperature then it is cold.} \\ \text{Contra positive: If something is at low temperature then it is cold. and converse: If something is not at low temperature then it is not cold.} \\ \text{Converse: If something is at low temperature then it is cold. and contra positive: If something is not at low temperature then it is not cold.} \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:
Something cold implies that it has low temperature.
here $p\rightarrow$ Something is cold. and
$q\rightarrow$ Something is at low temperature.
~$p\rightarrow$ Something is not cold.
~$q\rightarrow$ Something is not at low temperature.
$\therefore$ The converse of the given statement is
If something is at low temperature then it is cold.
The contra positive of the given statement is:
If something is not at low temperature then it is not cold.
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