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MHT CET202520 Apr 2025Evening ShiftMathematicsMathematical ReasoningActual

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

Options

  1. AThree vertices of a triangle are represented by cube roots of unity and the triangle is not an equilaterals tr
  2. BIf a triangle is an equilateral triangle then the three vertices of a triangle are represented by cube roots o
  3. CIf three vertices of triangle are not represented by cube roots of unity then the triangle is not an equilater
  4. DIf a triangle is not an equilateral triangle then the three vertices of the triangle can not be represented by

Correct answer

D. If a triangle is not an equilateral triangle then the three vertices of the triangle can not be represented by

Step-by-step solution

Let the statement be: If three vertices of a triangle are represented by cube roots of unity, then the triangle is an equilateral triangle. In symbolic form, let P represent three vertices of a triangle are represented by cube roots of unity and Q represent the triangle is an equilateral triangle . The given statement is P Q . Logically, P Q is equivalent to its contrapositive, Q P . Analyzing the options: Option A: P Q (the negation, not equivalent). Option B: Q P (the converse, not equivalent). Option C: P Q (the

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