Let A = \{3, 5, 7\}; B =\ x|x is an even whole number less than 11), C = \{2, 8, 10, 12\} and D =\ x|x is an odd whole number less than 12). Find A cap B.
Select the correct choice and fill in any answer boxes in your choice below.
OA. A cap B=\ Box\ (Use a comma to separate answers as needed.)
OB. The solution is the empty set.
OA. A cap B = {} (empty set)
To find A cap B, we need to find the intersection of set A and set B.
Set A = {3, 5, 7}
Set B = {x | x is an even whole number less than 11}
To find the intersection, we need to find the common elements in both sets.
The even whole numbers less than 11 are: 2, 4, 6, 8, 10
Checking each element in Set A:
- 3 is not an even number
- 5 is not an even number
- 7 is not an even number
None of the elements in Set A are in the set of even whole numbers less than 11.
Therefore, the intersection of A and B, A cap B, is the empty set.
The correct choice is:
OB. The solution is the empty set.
To find A cap B (the intersection of sets A and B), we need to determine the elements that are common to both A and B.
Set A = {3, 5, 7}
Set B = {x | x is an even whole number less than 11}
From set A, we only have odd whole numbers (3, 5, 7), so there are no elements in common with set B since set B contains only even numbers. Therefore, the intersection of A and B is the empty set.
Hence, the correct choice is OB. The solution is the empty set.