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If E = {x | x is a prime number less than 10}, what is the power set of E?
If E = {x | x is a prime number less than 10}, what is the power set of E?
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Practice Questions
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Q1
If E = {x | x is a prime number less than 10}, what is the power set of E?
{∅, {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}}
{∅, {2, 3, 5, 7}}
{∅, {2}, {3}, {5}, {7}}
{∅, {2, 3}, {5, 7}}
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The prime numbers less than 10 are {2, 3, 5, 7}. The power set has 2^4 = 16 elements.
Questions & Step-by-step Solutions
1 item
Q
Q: If E = {x | x is a prime number less than 10}, what is the power set of E?
Solution:
The prime numbers less than 10 are {2, 3, 5, 7}. The power set has 2^4 = 16 elements.
Steps: 6
Show Steps
Step 1: Identify the prime numbers less than 10. The prime numbers are 2, 3, 5, and 7.
Step 2: Write the set of prime numbers as E = {2, 3, 5, 7}.
Step 3: Determine the number of elements in set E. There are 4 elements in E.
Step 4: Calculate the power set of E. The power set is the set of all possible subsets of E.
Step 5: Use the formula for the number of subsets: 2^n, where n is the number of elements in the set. Here, n = 4.
Step 6: Calculate 2^4, which equals 16. This means the power set has 16 elements.
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