If H = {x, y}, how many subsets of H are also subsets of the power set of H?
Practice Questions
Q1
If H = {x, y}, how many subsets of H are also subsets of the power set of H?
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Questions & Step-by-Step Solutions
If H = {x, y}, how many subsets of H are also subsets of the power set of H?
Step 1: Identify the set H, which is given as H = {x, y}.
Step 2: Determine the power set of H. The power set includes all possible subsets of H, which are: ∅ (empty set), {x}, {y}, and {x, y}. So, the power set of H is {∅, {x}, {y}, {x, y}}.
Step 3: Identify the subsets of H. The subsets of H are: ∅, {x}, {y}.
Step 4: Count the number of subsets of H that are also in the power set of H. The subsets of H (∅, {x}, {y}) are all included in the power set of H.
Step 5: Conclude that there are 3 subsets of H that are also subsets of the power set of H.
