Let A = \{5, 7, 9\}; B =\ x|x; an even whole number less than 11), C = \{6, 8, 10, 12\} and D=\ x| xi! an odd whole number less than 12). Find AnB.
Select the correct choice and fill in any answer boxes in your choice below.
A. A cap B=\ Box\ (Use a comma to separate answers as needed.)
OB. The solution is the empty set.
A. A cap B = {6, 8}
To find the intersection of sets A and B (A ∩ B), we need to identify the elements that are common to both sets.
Set A = {5, 7, 9}
Set B = {x | x is an even whole number less than 11}
Since the elements in set B are not explicitly defined, we need to identify the even whole numbers less than 11 and then check which of those numbers are also in set A.
Even whole numbers less than 11: {2, 4, 6, 8, 10}
However, set A does not contain any of these numbers. Therefore, the intersection of sets A and B (A ∩ B) is the empty set.
Thus, the correct choice is:
B. The solution is the empty set.
There is no need to fill in any answer boxes as the solution is the empty set.
To find A ∩ B, or the intersection of sets A and B, we need to identify the elements that are common to both sets.
Set A is {5, 7, 9} and set B is {x | x is an even whole number less than 11}.
We can see that set B contains even numbers less than 11. Therefore, to find the intersection, we need to determine which elements from set A are also in set B.
Looking at set A, we see that none of its elements (5, 7, and 9) are even numbers less than 11. Thus, there are no elements common to both A and B.
Therefore, A ∩ B is the empty set, denoted by the symbol Ø.
The correct choice is:
B. The solution is the empty set.