If A = {1, 2, 3}, what is the power set of A?

If A = {1, 2, 3}, what is the power set of A?

Step 1: Identify the set A, which is {1, 2, 3}.
Step 2: Count the number of elements in set A. Here, there are 3 elements: 1, 2, and 3.
Step 3: Use the formula for the power set, which is 2^n, where n is the number of elements in the set.
Step 4: Calculate 2^3, since n = 3. This equals 8.
Step 5: List all the subsets of A. The subsets are: {}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, and {1, 2, 3}.
Step 6: Confirm that there are 8 subsets listed, which matches the calculation from Step 4.

Power Set – The power set of a set is the set of all possible subsets, including the empty set and the set itself.
Cardinality – Understanding that the number of subsets of a set with n elements is given by 2^n.