From the course: Programming Foundations: Discrete Mathematics

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Power sets

Power sets

From the course: Programming Foundations: Discrete Mathematics

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Power sets

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- [Voiceover] Next let's talk about power sets. A power set is the set of all subsets for a particular set including the empty set. The cardinality of a power set is two to the n, where n is the cardinality of the original set. For example, if the cardinality of set A is equal to three, which means that A has three elements, then the cardinality of the power set of A, which is denoted with a script P in front of the A, is equal to eight, because two-cubed is equal to eight. All right, if we're given the set A equals the set containing one, two, and three, let's write the power set of A. So we know, since there's three items, there's going to be eight sets. I'll start with the empty set so I don't forget that one. And this is going to be a set of sets. Next, I'll do each individual number. A set containing one, two, three. Now I'll start to do combinations of two. One and two. I definitely need to include a set that has all the original elements, and I think I'm done. If we count them…

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