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The number of sets of a set containing n-elements =2n .
A proper subset of a set is the set whose elements are in the given set, but it is not equal to the set.
Let S be a subset of A, S is called Proper subset if and only if it is a subset of A, and S ≠ A .
So, The number of proper subsets of a set containing n-elements is 2^{ n }- 1
As, The number of subsets contains a improper subset that is the set itself, so 1 is subtracted from number of total subsets to get number of proper subsets.
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Let A be the set A={1,5,10,15}
We have seen that the above set is the multiple of 5.
So, The equation satisfying this set is P=5n, n is the natural number and n<3
Put n=1 , P=5
Put n=2, P=10
Put n=3, P=15
A = { 1 , 5 , 10, 15} in set builder form is
A = { P :P = 5n where n<3}
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