Question

given the following sets, find the set $(a cup b) cap c$.

$u = \\{1, 2, 3, \dots, 6\\}$
$a = \\{1, 2, 3, 5\\}$
$b = \\{1, 2, 3\\}$
$c = \\{1, 2, 3, 4, 5\\}$

select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. $(a cup b) cap c = \boxed{}$
(use a comma to separate answers as needed.)

b. $(a cup b) cap c$ is the empty set.

Explanation:

Step1: Find $A \cup B$

$A \cup B = \{1,2,3,5\} \cup \{1,2,3\} = \{1,2,3,5\}$

Step2: Find $(A \cup B)'$

$(A \cup B)' = U - (A \cup B) = \{1,2,3,4,5,6\} - \{1,2,3,5\} = \{4,6\}$

Step3: Find $(A \cup B)' \cap C$

$(A \cup B)' \cap C = \{4,6\} \cap \{1,2,3,4,5\} = \{4\}$

Answer:

A. $(A \cup B)' \cap C = \{4\}$