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# For the statement "If a quadrilateral is a parallelogram then its diagonals bisect each other"' is the statement "If the diagonals of a quadrilateral do not bisect then it is not a parallelogram" contra positive or converse?

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• 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 a quadrilateral is a parallelogram then its diagonals bisect each other."
2. "If the diagonals of a quadrilateral do not bisect then it is not a parallelogram"
Here the second statement is contra positive of first one.
Because for first statement,
$p\rightarrow$ The quadrilateral is a parallelogram.
$q\rightarrow$ The diagonals of a quadrilateral bisect.
~$p\rightarrow$ The quadrilateral is not a parallelogram.
~$q\rightarrow$ The diagonals of a quadrilateral do not bisect.
The contra positive of ' If $p$ then $q$ is If ~$q$ then ~$p$
answered Jul 22, 2014
edited Jul 22, 2014

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