Question

given the following sets, find the set $(a cup b) cap c$.
$u = \\{1, 2, 3, \dots, 7\\}$
$a = \\{4, 5, 6, 7\\}$
$b = \\{3, 6, 7\\}$
$c = \\{1, 2, 3, 4, 5\\}$

select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. $(a cup b) cap c = \\{\\}$
(use a comma to separate answers as needed.)
b. $(a cup b) cap c$ is the empty set.

Explanation:

Step1: Find $A \cup B$

$A \cup B = \{3, 4, 5, 6, 7\}$

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

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

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

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

Answer:

A. $(A \cup B)' \cap C = \{1, 2\}$