If A = {x | x is an even number} and B = {x | x is a prime number}, what is A ∩

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Question: If A = {x | x is an even number} and B = {x | x is a prime number}, what is A ∩ B?

Options:

Correct Answer: {2}

Solution:

A ∩ B = {2} as 2 is the only even prime number.

If A = {x | x is an even number} and B = {x | x is a prime number}, what is A ∩ B?

If A = {x | x is an even number} and B = {x | x is a prime number}, what is A ∩ B?

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.

Set Theory – Understanding the intersection of sets and the properties of even and prime numbers.
Properties of Numbers – Knowledge of even numbers (divisible by 2) and prime numbers (greater than 1 with no divisors other than 1 and itself).