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Let X be a connected subset of real number’s. If every element of X is rational, then the cardinality of X is -
  • a)
    infinite
  • b)
    countably infinite
  • c)
    uncountable
  • d)
    1
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Let X be a connected subset of real number’s. If every element o...
We know if X ⊂ R then X is connected 
⇔ X be an interval
So if X be a non-empty and non-singleton connected set then X always has rational and irrational elements.
So there is only possibility for X is X be singleton 
Set i.e. X = {a} where a ∈ Q 
⇒ cardinality of X is 1.
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Let X be a connected subset of real number’s. If every element o...
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Let X be a connected subset of real number’s. If every element of X is rational, then the cardinality of X is -a)infiniteb)countably infinitec)uncountabled)1Correct answer is option 'D'. Can you explain this answer?
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