# What is the cardinality of the following set. P(S) stands for power set. Find p (p ((S) for S = {a, b}

Friday, July 23rd, 2010

### Solution:

1. The cardinality of a set is a measure of the “number of elements of the set”. For example, the set A = {2, 4, 6} contains = elements, and therefore A has a cardinality of 3.

2. Given a set S, the power set of S, written , P(S), is the set of all subsets of S, including the empty set and S itself.

3. If S={a, b}, then P(S) ={{},{a},{b},{a,b}} and the Cardinality of P(S) is 4.

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