What Is A Power Set? And Please Give An Example Of Power Set.

What is a power set? And please give an example of power set.

 

Answer:

For the set {a,b,c}:

The empty set {} is a subset of {a,b,c}

And these are subsets: {a}, {b} and {c}

And these are also subsets: {a,b}, {a,c} and {b,c}

And {a,b,c} is a subset of {a,b,c}

And altogether we get the Power Set of {a,b,c}:

P(S) = { {}, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c} }

Step-by-step explanation:

Example: The shop has banana, chocolate and lemon ice cream.

 

What do you order?

Nothing at all: {}

Or maybe just banana: {banana}. Or just {chocolate} or just {lemon}

Or two together: {banana,chocolate} or {banana,lemon} or {chocolate,lemon}

Or all three! {banana, chocolate,lemon}