If A = {x | x is a natural number and x < 5} and B = {x | x is a natural number and x > 2}, what is A ∩ B?
Practice Questions
1 question
Q1
If A = {x | x is a natural number and x < 5} and B = {x | x is a natural number and x > 2}, what is A ∩ B?
{1, 2}
{3, 4}
{2, 3, 4}
{1, 2, 3, 4}
Set A = {1, 2, 3, 4} and set B = {3, 4, 5, ...}. The intersection A ∩ B = {3, 4}.
Questions & Step-by-step Solutions
1 item
Q
Q: If A = {x | x is a natural number and x < 5} and B = {x | x is a natural number and x > 2}, what is A ∩ B?
Solution: Set A = {1, 2, 3, 4} and set B = {3, 4, 5, ...}. The intersection A ∩ B = {3, 4}.
Steps: 5
Step 1: Identify the elements of set A. A is defined as the set of natural numbers less than 5. The natural numbers less than 5 are 1, 2, 3, and 4. So, A = {1, 2, 3, 4}.
Step 2: Identify the elements of set B. B is defined as the set of natural numbers greater than 2. The natural numbers greater than 2 start from 3 and go on indefinitely. So, B = {3, 4, 5, ...}.
Step 3: Find the intersection of sets A and B. The intersection A ∩ B includes only the elements that are present in both sets A and B.
Step 4: Compare the elements of A and B. The elements in A are {1, 2, 3, 4} and the elements in B are {3, 4, 5, ...}. The common elements are 3 and 4.
Step 5: Write the intersection. Therefore, A ∩ B = {3, 4}.
