MHT CET202523 Apr 2025Morning ShiftMathematicsMathematical ReasoningActual
Which of the following is the negation of the statement " For all M >0 , there exist x s such that x M "
Options
- AM >0 such that x M for all x ~s
- BM >0, x ~s such that x M
- CM >0 such that x < M for all x ~s
- DM >0 , there exist x ~s such that x < M
Correct answer
C. M >0 such that x < M for all x ~s
Step-by-step solution
The statement " For all M>0 , there exists x s such that x M " has logical structure M>0, x s : x M . Negating quantifiers transforms to and vice versa, while the inequality x M becomes x The negation is therefore M>0, x s : x This corresponds to option C : M>0 such that x