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Let X be a proper closed subset of [0,1]. Which of the following statements is always true ?
  • a)
    The set X is countable
  • b)
    There is x ∈ X such that X-{x} is closed
  • c)
    The set X contains an open interval
  • d)
    None of the above
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Let X be a proper closed subset of [0,1]. Which of the following state...
 proper closed subset of [0,1] but X not countable

 be a proper closed subset of [0,1] but it cannot contain an open interval.
⇒ None of given options are true.
⇒ (d) is correct.
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Most Upvoted Answer
Let X be a proper closed subset of [0,1]. Which of the following state...
B) There is x in [0,1] such that x is not in X.

This statement is always true because X is a proper closed subset of [0,1], meaning that X does not contain all the points in [0,1]. Therefore, there must be at least one point x in [0,1] that is not in X.
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Let X be a proper closed subset of [0,1]. Which of the following statements is always true ?a)The set X is countableb)There is x ∈ X such that X-{x} is closedc)The set X contains an open intervald)None of the aboveCorrect answer is option 'D'. Can you explain this answer?
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Let X be a proper closed subset of [0,1]. Which of the following statements is always true ?a)The set X is countableb)There is x ∈ X such that X-{x} is closedc)The set X contains an open intervald)None of the aboveCorrect answer is option 'D'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Let X be a proper closed subset of [0,1]. Which of the following statements is always true ?a)The set X is countableb)There is x ∈ X such that X-{x} is closedc)The set X contains an open intervald)None of the aboveCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let X be a proper closed subset of [0,1]. Which of the following statements is always true ?a)The set X is countableb)There is x ∈ X such that X-{x} is closedc)The set X contains an open intervald)None of the aboveCorrect answer is option 'D'. Can you explain this answer?.
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