If A = {x | x is an even number} and B = {x | x is a prime number}, what is A ∩ B?
Practice Questions
1 question
Q1
If A = {x | x is an even number} and B = {x | x is a prime number}, what is A ∩ B?
{2}
{2, 3}
{2, 4}
{}
A ∩ B = {2} as 2 is the only even prime number.
Questions & Step-by-step Solutions
1 item
Q
Q: If A = {x | x is an even number} and B = {x | x is a prime number}, what is A ∩ B?
Solution: A ∩ B = {2} as 2 is the only even prime number.
Steps: 6
Step 1: Understand what set A is. Set A contains all even numbers. Examples are 0, 2, 4, 6, 8, etc.
Step 2: Understand what set B is. Set B contains all prime numbers. Prime numbers are numbers greater than 1 that have no divisors other than 1 and themselves. Examples are 2, 3, 5, 7, 11, etc.
Step 3: Identify the intersection of sets A and B, which is written as A ∩ B. This means we are looking for numbers that are both even and prime.
Step 4: Check the even numbers in set A to see if they are also prime. The even numbers are 0, 2, 4, 6, 8, etc.
Step 5: Determine if each even number is prime. The only even number that is prime is 2, because it can only be divided by 1 and itself.
Step 6: Conclude that the intersection A ∩ B contains only the number 2.
