Let S be a non-empty subset of IR. Consider the following statement : p : There is a rational number x S such that x>0. Which of the following statement is the negation of the statement p ?

MHT CET 2024 Mathematics question

Not in JEE syllabus

Let S be a non-empty subset of IR. Consider the following statement : p : There is a rational number such that . Which of the following statement is the negation of the statement p ?

(A)There is a rational number such that
(B)There is no rational number such that
(C)Every rational number satisfies Correct
(D) and is not a rational number

Answer: (C)

Solution

The statement has the form . Its negation is obtained by changing to and negating the condition to : , i.e. "Every rational number satisfies ", option (C). Option (A) only

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Question ID VK-099881