JEE Main & Advanced Mathematics Mathematical Logic and Boolean Algebra Question Bank Mock Test - Mathematical Reasoning

  • question_answer
    Let S be a non-empty subset of R. Consider the following statement: P: There is a rational number \[x\in S\] such that\[x>0\]. Which of the following statements is the negation of the statement p?

    A) \[x\in S\] and \[x\le 0\Rightarrow x\] is not rational.

    B) There is a rational number \[x\in S\] such that \[x\le 0\].

    C) There is no rational number \[x\in S\] such that\[x\le 0\].

    D) Every rational number \[x\in S\]satisfies\[x\le 0\].

    Correct Answer: D

    Solution :

    [d] P: There is a rational number \[x\in S\]such that\[x>0\]. ~ P: Every rational number \[x\in S\] satisfies \[x\le 0.\]

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