Saturday

October 10, 2015
Posted by **Peter** on Saturday, June 11, 2011 at 5:29am.

- algebra -
**Peter**, Saturday, June 11, 2011 at 5:36amuse 2 as the base!, 2 raise to the power of n, where n is the number of elements in a set.

- algebra -
**MathMate**, Sunday, June 12, 2011 at 8:45amThe power set is the set of all possible subsets of a given set of cardinality n (contains n elements). The power set has a cardinality of 2^n.

To find the all elements of the power set of a given set A, we start with the null set, and add one element at a time.

{∅}

{∅,a}

{∅,a, b,{a,b}}

{∅,a, b,{a,b}, c,{a,c},{b,c},{a,b,c}}

...

and so on.

We see that the introduction of each element of A doubles the number of subsets, hence the total number of 2^n.