MHT CET · Maths · Mathematical Reasoning
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
- A 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. - B 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. - C 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. - D 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.
Answer & Solution
Correct Answer
(C) 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.
Step-by-step Solution
Detailed explanation
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
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