The equivalent statement of "If three vertice | vedclass

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Question

(D) Let $P$ be the statement: "Three vertices of a triangle are represented by cube roots of unity".Let $Q$ be the statement: "The triangle is an equi

Vedclass · Accepted Answer

If a triangle is not an equilateral triangle,then the three vertices of the triangle cannot be represented by cube roots of unity.

Vedclass · Answer

(D) Let $P$ be the statement: "Three vertices of a triangle are represented by cube roots of unity".Let $Q$ be the statement: "The triangle is an equilateral triangle".The given statement is of the form $P \implies Q$.The contrapositive of a conditional statement $P \implies Q$ is $
eg Q \implies 
eg P$,which is logically equivalent to the original statement.Here,$
eg Q$ is: "The triangle is not an equilateral triangle".Here,$
eg P$ is: "The three vertices of the triangle are not represented by cube roots of unity".Thus,the equivalent statement is $
eg Q \implies 
eg P$,which is: "If a triangle is not an equilateral triangle,then the three vertices of the triangle cannot be represented by cube roots of unity".Therefore,the correct option is $D$.

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

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