For statement; If a quadrilateral $A B C D$ is a rhombus then its opposite sides are parallel", its…

For statement; If a quadrilateral $A B C D$ is a rhombus then its opposite sides are parallel", its contrapositive and converse are respectively given by
  1. i. If opposite sides of a quadrilateral $A B C D$ are not parallel, then quadrilateral $A B C D$ is a rhombus. ii. If opposite sides of a quadrilateral $A B C D$ are not parallel, then the quadrilateral $A B C D$ is a rhombus.
  2. i. If opposite sides of a quadrilateral $A B C D$ are not parallel then quadrilateral $A B C D$ is not rhombus. ii. If opposite sides of a quadrilateral $A B C D$ are parallel, then quadrilateral $A B C D$ is not rhombus.
  3. i. If opposite sides of a quadrilateral $A B C D$ are parallel, then quadrilateral $A B C D$ is not a rhombus. ii. If opposite sides of a quadrilateral $A B C D$ are parallel, then quadrilateral $A B C D$ is a rhombus.
  4. i. If opposite sides of a quadrilateral $A B C D$ are parallel, then quadrilateral $A B C D$ is not a rhombus. ii. If opposite sides of a quadrilateral $A B C D$ are not parallel, then quadrilateral $A B C D$ is a rhombus.

Solution

Contrapositive of $p \rightarrow q$ is $\sim q \rightarrow \sim p$ and converse of $p \rightarrow q$ is $q \rightarrow p$ Hence, option (C) is correct

Asked in: MHT CET 2022 (11 Aug Shift 1)

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