Without writing them all out, what is the number of subsets of set A = {tongue, ear, mouth, eye, nose, cheek, forehead, neck, shoulder}?
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?
2^9=512 subsets
To find the number of subsets of a set, we can use the formula:
Number of subsets = 2^n
where n is the number of elements in the set.
In this case, set A has 9 elements (tongue, ear, mouth, eye, nose, cheek, forehead, neck, shoulder), so the number of subsets is:
Number of subsets = 2^9
Calculating 2^9, we find:
Number of subsets = 512
Therefore, there are 512 subsets of set A = {tongue, ear, mouth, eye, nose, cheek, forehead, neck, shoulder}.