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What is the power set of the empty set ∅?

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Question: What is the power set of the empty set ∅?

Options:

  1. {∅}
  2. {∅, {∅}}
  3. ∅
  4. {∅, ∅}

Correct Answer: {∅}

Solution: 

The power set of the empty set contains only the empty set itself: {∅}.

What is the power set of the empty set ∅?

Practice Questions

Q1
What is the power set of the empty set ∅?
  1. {∅}
  2. {∅, {∅}}
  3. ∅
  4. {∅, ∅}

Questions & Step-by-Step Solutions

What is the power set of the empty set ∅?
  • Step 1: Understand what a set is. A set is a collection of distinct objects.
  • Step 2: Recognize what the empty set (∅) is. The empty set is a set that contains no elements.
  • Step 3: Learn about the power set. The power set of a set is the set of all possible subsets of that set.
  • Step 4: Identify the subsets of the empty set. The only subset of the empty set is the empty set itself.
  • Step 5: Write the power set of the empty set. Since the only subset is the empty set, the power set is {∅}.
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