Which of the following does not have a proper subset?

{x : x ϵ Q}

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{x : x ϵ N, 3 < x < 4}

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{x : x ϵ Q, 3 < x < 4}

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None of these

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Solution

The correct option is A ${x : x ϵ N, 3 < x < 4}$
The set ${x : x ϵ N, 3 < x < 4}$ is empty because there is no natural number between 3 and 4.
$∴$ This set cannot have a proper subset.

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