List all subsets of the following set: {dog, cat, fish}

There are 8 subsets here. We have the original set {dog, cat, fish} which we can list the items in any order we want.

Then we have the set of items where we only pick two pets

{dog, cat}

{dog, fish}

{cat, fish}

the order for any given set does not matter

Then we have the set of just one pet only

{dog}

{cat}

{fish}

And finally, we have the empty set { } which is just curly braces with nothing inside.

In summary, we have these 8 subsets

{dog, cat, fish}

{dog, cat}, {dog, fish}, {cat, fish}

{dog}, {cat}, {fish}

{ }

Note how this is equal to 2^n = 2^3 = 8. The n = 3 indicates how many items are in the original set. The set of all possible subsets is known as the power set.

Dog, cat

Dog, fish

Cat, fish

Dog, fish, cat

Fish, cat, dog

Cat, dog, fish

Fish, dog, cat