MHT CET 2025 Mathematics question

Not in JEE syllabus

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 a triangle can not be represented by cube roots of unity.Correct

Answer: (D)

Solution

The statement has the form with : "three vertices are cube roots of unity" and : "the triangle is equilateral". The logically equivalent statement is the contrapositive : "If the triangle is not equilateral, then its three vertices cannot be the cube roots of unity",

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Question ID VK-101240