DrDelMath

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1. Find all the subsets of {a, b, c}.
Begin by thinking about the question and writing down the observations.
We know from general knowledge about subsets that and {a, b, c} are subsets of {a, b, c}.
One of these sets has 0 elements (the minimum number) while the other has 3 elements (the maximum number).
Other subsets must be singleton sets or they must contain exactly two elements.
The singleton subsets of {a, b, c} are {a}, {b}, and {c}.
The subsets with two elements are {a, b}, {a, c} and {b, c}.
The complete collection of subsets of {a, b, c} are:
, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, and {a, b, c}.

Observe that subsets of {a, b, c} are mathematical objects and we have just written a collection of those objects, so we must be talking about a set.
The set of all subsets of a given set A is called the power set of A. It has some importance in other parts of mathematics.
So the power set of {a, b, c} is:
{ , {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, and {a, b, c} }.