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

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

Options:

{∅, {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}}

Correct Answer: {∅, {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}}

Solution:

The prime numbers less than 10 are {2, 3, 5, 7}. The power set has 2^4 = 16 elements.

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}}

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

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.

Set Theory – Understanding sets, subsets, and the concept of a power set, which is the set of all subsets of a given set.
Prime Numbers – Identifying prime numbers and understanding their properties, particularly in relation to the specified range.
Exponential Growth – Calculating the number of subsets in a power set using the formula 2^n, where n is the number of elements in the original set.