If A = {x | x is an even integer} and B = {x | x is a prime number}, what is A ∩ B?
Practice Questions
1 question
Q1
If A = {x | x is an even integer} and B = {x | x is a prime number}, what is A ∩ B?
{2}
{2, 3}
{2, 4}
{}
The only even prime number is 2, so A ∩ B = {2}.
Questions & Step-by-step Solutions
1 item
Q
Q: If A = {x | x is an even integer} and B = {x | x is a prime number}, what is A ∩ B?
Solution: The only even prime number is 2, so A ∩ B = {2}.
Steps: 5
Step 1: Understand what set A is. Set A contains all even integers, which are numbers like -4, -2, 0, 2, 4, 6, etc.
Step 2: Understand what set B is. Set B contains all prime numbers, which are numbers greater than 1 that have no divisors other than 1 and themselves, like 2, 3, 5, 7, 11, etc.
Step 3: Identify the common elements between set A and set B. We need to find numbers that are both even integers and prime numbers.
Step 4: Check the even integers in set A. The only even prime number is 2, because all other even numbers can be divided by 2, making them not prime.
Step 5: Conclude that the intersection of set A and set B, denoted as A ∩ B, contains only the number 2.
