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

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

Options:

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

Correct Answer: {∅, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Solution: 

The power set of a set with n elements has 2^n subsets. Here, n=3, so the power set has 2^3 = 8 subsets.

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

Practice Questions

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

Questions & Step-by-Step Solutions

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.
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