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

Practice Questions

1 question

{{2}, {3}, {5}, {7}}
{{}, {2}, {3}, {5}, {7}}
{{2, 3, 5, 7}, {2, 3}, {5, 7}}
{{2, 3, 5, 7}, {}}

Questions & Step-by-step Solutions

1 item

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

Solution: The set C = {2, 3, 5, 7}. The power set of C includes all subsets, including the empty set, so it is {{}, {2}, {3}, {5}, {7}, {2, 3}, {2, 5}, {2, 7}, {3, 5}, {3, 7}, {5, 7}, {2, 3, 5}, {2, 3, 7}, {2, 5, 7}, {3, 5, 7}, {2, 3, 5, 7}}.

Steps: 9

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.

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

Practice Questions

Questions & Step-by-step Solutions

Related Questions

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?