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