Relations And Functions

  • Question
    CBSEENMA11013295

    Which of the following are examples of null set?

    { x : x is a natural numbers, x < 5 and x > 7 }

    Solution

    Let      space space space space space space space space space straight D space space equals space space left curly bracket space straight x space colon space straight x space element of space bold N bold comma bold space bold x bold space bold less than bold space bold 5  and simultaneously x > 7}
    There is no natural number which is simultaneously < 5 and  > 7.
    rightwards double arrow      space space space space space space space space straight D space space equals space open curly brackets space space close curly brackets space equals space straight ϕ
    Hence, D is a null set.

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