Question: Write the resulting set using the listing method. \(\{4, 6\} \cap \{0, 1, 6\}\) Select the…

Write the resulting set using the listing method.

\(\{4, 6\} \cap \{0, 1, 6\}\)

Select the correct choice below and fill in any answer boxes present in your choice.

A. \(\{4, 6\} \cap \{0, 1, 6\} = \{\}\) (Use a comma to separate answers as needed.)

B. \(\{4, 6\} \cap \{0, 1, 6\}\) is the empty set.

Solution

To find the resulting set using the listing method, we need to determine the intersection of the sets \(\{4, 6\}\) and \(\{0, 1, 6\}\). The intersection of two sets contains all elements that are common to both sets. 1. Identify the common elements between the two sets: - Check each element in the first set \(\{4, 6\}\) to see if it is in the second set \(\{0, 1, 6\}\). 2. The element \(6\) is present in both sets. Therefore, the intersection is: \[ \{6\} \] So, the correct choice is: A. \(\{4, 6\} \cap \{0, 1, 6\} = \{6\}\)