If E = {x | x is a prime number less than 10}, what is E?
Practice Questions
Q1
If E = {x | x is a prime number less than 10}, what is E?
{2, 3, 5, 7}
{1, 2, 3, 4}
{2, 4, 6, 8}
{3, 5, 7}
Questions & Step-by-Step Solutions
If E = {x | x is a prime number less than 10}, what is E?
Step 1: Understand what a prime number is. A prime number is a number greater than 1 that has no positive divisors other than 1 and itself.
Step 2: List the numbers less than 10. These numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9.
Step 3: Check each number to see if it is prime.
Step 4: 1 is not prime because it only has one divisor (1).
Step 5: 2 is prime because it has two divisors (1 and 2).
Step 6: 3 is prime because it has two divisors (1 and 3).
Step 7: 4 is not prime because it has three divisors (1, 2, and 4).
Step 8: 5 is prime because it has two divisors (1 and 5).
Step 9: 6 is not prime because it has four divisors (1, 2, 3, and 6).
Step 10: 7 is prime because it has two divisors (1 and 7).
Step 11: 8 is not prime because it has four divisors (1, 2, 4, and 8).
Step 12: 9 is not prime because it has three divisors (1, 3, and 9).
Step 13: Collect all the prime numbers found: 2, 3, 5, and 7.
Step 14: Write the set E as {2, 3, 5, 7}.
Prime Numbers – A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. The only divisors of a prime number are 1 and itself.
Set Notation – Set notation is a mathematical way to describe a collection of objects, often defined by a property that its members share.