If set P = {x | x is an even number less than 10} and set Q = {x | x is a prime
Practice Questions
Q1
If set P = {x | x is an even number less than 10} and set Q = {x | x is a prime number less than 10}, what is the intersection of sets P and Q?
{2, 4, 6, 8}
{2, 3, 5, 7}
{2}
{4, 6, 8}
Questions & Step-by-Step Solutions
If set P = {x | x is an even number less than 10} and set Q = {x | x is a prime number less than 10}, what is the intersection of sets P and Q?
Step 1: Identify the elements of set P. Set P includes all even numbers less than 10. The even numbers less than 10 are 0, 2, 4, 6, and 8. So, P = {0, 2, 4, 6, 8}.
Step 2: Identify the elements of set Q. Set Q includes all prime numbers less than 10. The prime numbers less than 10 are 2, 3, 5, and 7. So, Q = {2, 3, 5, 7}.
Step 3: Find the intersection of sets P and Q. The intersection includes elements that are in both sets P and Q.
Step 4: Compare the elements of P and Q. The only number that appears in both sets is 2.
Step 5: Conclude that the intersection of sets P and Q is {2}.
Set Theory – Understanding the definition of sets, intersections, and the properties of even and prime numbers.
Even Numbers – Recognizing that even numbers are divisible by 2.
Prime Numbers – Identifying prime numbers as those greater than 1 that have no divisors other than 1 and themselves.
