Question

Without writing them all out, what is the number of subsets of set A = {tongue, ear, mouth, eye, nose, cheek, forehead, neck, shoulder}?

Answer 1

A one-element set {a} can form two subsets: {∅}, {a}
A two-element set {a,b} can double the above list by tagging a b to each of the above two sets, thereby doubling the number: {∅},{a},{b},{a,b} for a total of 2²=4 sets.

Similarly, by doubling again, the number of subsets of a three-element set is 2³=8...

Thus, we conclude that the number of subsets (including ∅) of a set of cardinality n is 2ⁿ.

The given set has 9 elements, so how many subsets can be made?

Answer 2

2^9=512 subsets