MHT CET · Maths · Mathematical Reasoning

The equivalent statement of " If three vertices of a triangle are represented by cube roots of unity, then the triangle is an equilateral triangle " is

A Three vertices of a triangle are represented by cube roots of unity and the triangle is not an equilaterals triangle.
B If a triangle is an equilateral triangle then the three vertices of a triangle are represented by cube roots of unity.
C If three vertices of triangle are not represented by cube roots of unity then the triangle is not an equilateral triangle.
D If a triangle is not an equilateral triangle then the three vertices of the triangle can not be represented by cube roots of unity.

Verified Solution

Answer & Solution

Correct Answer

(D) If a triangle is not an equilateral triangle then the three vertices of the triangle can not be represented by cube roots of unity.

Step-by-step Solution

Detailed explanation

If P then Q is logically equivalent to If not Q then not P (Contrapositive). Original statement: "If P (three vertices of a triangle are represented by cube roots of unity), then Q (the triangle is an equilateral triangle)".

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Explore more questions on app

From MHT CET

Explore more questions on app