For the statement: "If a quadrilateral ABCD i | vedclass

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Question

(C) Let $p$ be the statement: "$A$ quadrilateral $ABCD$ is a rhombus".Let $q$ be the statement: "Its opposite sides are parallel".The given statement

Vedclass · Accepted Answer

$i$. If opposite sides of a quadrilateral $ABCD$ are not parallel,then quadrilateral $ABCD$ is not a rhombus. $ii$. If opposite sides of a quadrilateral $ABCD$ are parallel,then quadrilateral $ABCD$ is a rhombus.

Vedclass · Answer

(C) Let $p$ be the statement: "$A$ quadrilateral $ABCD$ is a rhombus".Let $q$ be the statement: "Its opposite sides are parallel".The given statement is $p \rightarrow q$.The contrapositive of $p \rightarrow q$ is $\sim q \rightarrow \sim p$,which translates to: "If the opposite sides of a quadrilateral $ABCD$ are not parallel,then the quadrilateral $ABCD$ is not a rhombus".The converse of $p \rightarrow q$ is $q \rightarrow p$,which translates to: "If the opposite sides of a quadrilateral $ABCD$ are parallel,then the quadrilateral $ABCD$ is a rhombus".Comparing these with the given options,option $C$ is correct.

For the statement: "If a quadrilateral $ABCD$ is a rhombus,then its opposite sides are parallel",its contrapositive and converse are respectively given by:

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