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

Write the contrapositive and converse of the statement: "If $x$ is prime then $x$ is odd."

$\begin{array}{1 1} \text{Converse: If x is odd then x is prime. and Contra positive: If x is not odd then x is not a prime number.} \\ \text{Converse: If x is not odd then x is prime. and Contra positive: If x is not odd then x is not a prime number.} \\\text{ Converse: If x is odd then x is prime. and Contra positive: If x is not odd then x is a prime number.} \\ \text{Contra positive: If x is odd then x is prime. and Converse: If x is not odd then x is not a prime number.} \end{array} $

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A)
Toolbox:
  • Converse of: If $p$ then $q$ is If $q$ then $p.$
  • Contra positive of If $p$ then $q$ is If ~$q$ then ~$p.$
The given statement is : If $x$ is prime then $x$ is odd.
Here $p\rightarrow$ $x$ is prime.
$q\rightarrow$ $x$ is odd.
$\Rightarrow\:$ ~$p\rightarrow\:$ $x$ is not prime and
~$q\rightarrow\:$ $x$ is not odd.
$\therefore$ The converse of this statement is:
If $x$ is odd then $x$ is prime. and
The contra positive of this statement is:
If $x$ is not odd then $x$ is not a prime number.
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