If B = {a, b}, what is the power set of B?

Practice Questions

Q1
If B = {a, b}, what is the power set of B?
  1. {∅, {a}, {b}, {a, b}}
  2. {∅, {a, b}}
  3. {a, b}
  4. {a, b, ∅}

Questions & Step-by-Step Solutions

If B = {a, b}, what is the power set of B?
Correct Answer: {∅, {a}, {b}, {a, b}}
  • Step 1: Understand what a power set is. A power set is the set of all possible subsets of a given set.
  • Step 2: Identify the original set B. In this case, B = {a, b}.
  • Step 3: List all possible subsets of B. The subsets include: the empty set (∅), the set containing just 'a' ({a}), the set containing just 'b' ({b}), and the set containing both 'a' and 'b' ({a, b}).
  • Step 4: Combine all the subsets into one set. The power set of B is {∅, {a}, {b}, {a, b}}.
  • Power Set – The power set of a set is the set of all possible subsets, including the empty set and the set itself.
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