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

Write the converse and contra positive statement of the statement " If the two lines are parallel then they do not intersect in the same plane."

$\begin{array}{1 1}\text{Converse: If the two lines do not intersect in the same plane then the lines are parallel. contra positive: If the two lines intersect in the same plane then the lines are parallel.} \\ \text{Converse: If the two lines do not intersect in the same plane then the lines are parallel. contra positive: If the two lines intersect in the same plane then the lines are not parallel.} \\ \text{Contra positive: If the two lines do not intersect in the same plane then the lines are parallel. converse: If the two lines intersect in the same plane then the lines are not parallel.} \\\text{Converse: If the two lines intersect in the same plane then the lines are parallel. contra positive: If the two lines intersect in the same plane then the lines are not parallel.}\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:
If the two lines are parallel then they do not intersect in the same plane.
Here $p\rightarrow$ Two lines are parallel.
$q\rightarrow$ Two lines do not intersect in the same plane.
~$p\rightarrow$ Two lines are not parallel.
~$q\rightarrow$ Two lines do not intersect in the same plane.
$\therefore$ The converse of the given statement is:
If the two lines do not intersect in the same plane then the lines are parallel.
The contra positive statement of the given statement is:
If the two lines intersect in the same plane then the lines are not parallel.
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