The power set of a set with n elements has 2^n elements. For {1, 2}, the power set is {∅, {1}, {2}, {1, 2}}.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the power set of the set {1, 2}?
Solution: The power set of a set with n elements has 2^n elements. For {1, 2}, the power set is {∅, {1}, {2}, {1, 2}}.
Steps: 6
Step 1: Identify the original set. In this case, the set is {1, 2}.
Step 2: Count the number of elements in the set. There are 2 elements (1 and 2).
Step 3: Use the formula for the power set, which is 2 raised to the number of elements (n). Here, n = 2, so we calculate 2^2.
Step 4: Calculate 2^2, which equals 4. This means the power set will have 4 elements.
Step 5: List all possible subsets of the original set. The subsets are: the empty set (∅), the set containing just 1 ({1}), the set containing just 2 ({2}), and the set containing both elements ({1, 2}).
Step 6: Combine all the subsets into the power set. The power set is {∅, {1}, {2}, {1, 2}}.
