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
- AThree vertices of a triangle are represented by cube roots of unity and the triangle is not an equilaterals tr
- BIf a triangle is an equilateral triangle then the three vertices of a triangle are represented by cube roots o
- CIf three vertices of triangle are not represented by cube roots of unity then the triangle is not an equilater
- 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