Question

define sets u, a, b, and c as shown below. find (a∪b∪c).
u = {a, b, c, d, e, f, g, h} a = {f, g, h} b = {a, g, h} c = {a, b, c, d, e}
select the correct choice below and, if necessary, fill in the answer box within your choice.
a. (a∪b∪c) = { } (use a comma to separate answers as needed. type each answer only once.)
b. (a∪b∪c) = ∅

Explanation:

Step1: Find $A\cup B\cup C$

Combine all unique elements from A, B, C:
$A\cup B\cup C = \{f,g,h,a,b,c,d,e\}$

Step2: Identify universal set U

$U = \{a,b,c,d,e,f,g,h\}$

Step3: Compute complement $(A\cup B\cup C)'$

Elements in U not in $A\cup B\cup C$:
$(A\cup B\cup C)' = U - (A\cup B\cup C)$

Answer:

B. $(A\cup B\cup C)' = \emptyset$