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If C = {x | x is a prime number less than 10}, what is the power set of C?

Practice Questions

Q1
If C = {x | x is a prime number less than 10}, what is the power set of C?
  1. {{2}, {3}, {5}, {7}}
  2. {{}, {2}, {3}, {5}, {7}}
  3. {{2, 3, 5, 7}, {2, 3}, {5, 7}}
  4. {{2, 3, 5, 7}, {}}

Questions & Step-by-Step Solutions

If C = {x | x is a prime number less than 10}, what is the power set of C?
  • Step 1: Identify the prime numbers less than 10. The prime numbers are 2, 3, 5, and 7.
  • Step 2: Create the set C with these prime numbers. So, C = {2, 3, 5, 7}.
  • Step 3: Understand what a power set is. The power set is the set of all possible subsets of a set, including the empty set.
  • Step 4: List all subsets of C. Start with the empty set: {}.
  • Step 5: Add single-element subsets: {2}, {3}, {5}, {7}.
  • Step 6: Add two-element subsets: {2, 3}, {2, 5}, {2, 7}, {3, 5}, {3, 7}, {5, 7}.
  • Step 7: Add three-element subsets: {2, 3, 5}, {2, 3, 7}, {2, 5, 7}, {3, 5, 7}.
  • Step 8: Add the full set as a subset: {2, 3, 5, 7}.
  • Step 9: Combine all the subsets to form the power set of C.
  • Set Theory – Understanding sets, subsets, and the concept of a power set.
  • Prime Numbers – Identifying prime numbers and their properties.
  • Combinatorics – Calculating the number of subsets of a set.
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