MHT CET202525 Apr 2025Morning ShiftMathematicsMathematical ReasoningActual
The negation of the statement "The triangle is an equilateral or isosceles triangle and the triangle is not isosceles and it is right angled" is
Options
- AThe triangle is not an equilateral or not an isosceles triangle or it is not an isosceles or it is not right a
- BThe triangle is not an equilateral triangle or not isosceles triangle and it is isosceles or it is not right a
- CIf the triangle is an equilateral triangle or an isosceles triangle then it is an isosceles triangle or not ri
- DIf the triangle is an equilateral triangle or an isosceles triangle then it is not isosceles triangle and it i
Correct answer
C. If the triangle is an equilateral triangle or an isosceles triangle then it is an isosceles triangle or not ri
Step-by-step solution
Define the propositions: P: the triangle is equilateral Q: the triangle is isosceles R: the triangle is right-angled The statement S is (P Q) ( Q R) . Applying De Morgan's Law to the negation: S [(P Q) ( Q R)] (P Q) ( Q R) Applying De Morgan's Law to each disjunct: (P Q) P Q ( Q R) Q R Q R Combining these yields: S ( P Q) (Q R) Option C expresses the implication (P Q) (Q R) , which is logically equivalent to (P Q) (Q R) Applying De Morgan's Law gives ( P Q) (Q R) This matches our derived negation exactly, making Op