belaa3sM8aerimdenB
belaa3sM8aerimdenB belaa3sM8aerimdenB
  • 31-08-2016
  • Mathematics
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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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HomertheGenius
HomertheGenius HomertheGenius
  • 03-09-2017
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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