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Which of the following cannot be the negation of the statement “All angles are equal in equilateral triangle”?

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in Mathematics - Class 11 by (789k points)
Which of the following cannot be the negation of the statement “All angles are equal in equilateral triangle”?

(a) There is at least one angle different in equilateral triangle

(b) It is false that all angles are equal in equilateral triangle

(c) It is not the case that all angles are equal in equilateral triangle

(d) All angles are unequal in equilateral triangle

This question was addressed to me in examination.

The doubt is from Mathematical Reasoning topic in portion Mathematical Reasoning of Mathematics – Class 11

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Right choice is (d) All angles are unequal in equilateral triangle

To explain I would say: Negation of all angles is ‘not all angles’. So, negation of the given statement is “There is at least one angle different in equilateral triangle”, “It is false that all angles are equal in equilateral triangle”, “It is not the case that all angles are equal in equilateral triangle”. But “All angles are unequal in equilateral triangle” cannot be the negation of given statement as this does not include isosceles triangles.

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