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27 October, 08:45

How many elements must a set have if the number of proper subsets of the set 1/2 of the total number of subsets of the set?

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  1. 27 October, 08:50
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    A proper subset of a set A is a subset that is strictly contained in A and excludes at least one member of A. The empty set is also a proper subset of any nonempty set.

    So there is only 1 element that a set must have if the number of proper subsets is 1/2 of the total number of subsets.

    For example: A = { 4 }

    Proper subset : { } (1)

    All subsets: { }, { 4 } (2)

    1 = 1/2 * 2

    Answer: 1 element.
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