Question

Let X = {a,b,c}. What is the cardinality of P(X)? (Note that P(X) denotes the powerset of set S.)

Answer 1

Answer: 8

Step-by-step explanation

The power set is the set of all possible subsets of the given set.

The original set is {a,b,c}. A subset would consist of items chosen from here. So {a,b} is one possible subset because 'a' and 'b' are found in the original set. A non-example would be {a,d} because d is not found in the original set.

Here's a list of all 8 subsets. The { } at the end is the empty set. The empty set is a subset of any set. Any set is a subset of itself.

1. {a,b,c}
2. {a,b}
3. {a,c}
4. {b,c}
5. {a}
6. {b}
7. {c}
8. { }

The formula is 2^n where n is the number of items in the original set. We have n = 3 items lead to 2^n = 2^3 = 8 different subsets.