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 = {b, e, g} b = {a, e, g} c = {a, c, d, f, h}
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:
$A\cup B\cup C = \{b,e,g\} \cup \{a,e,g\} \cup \{a,c,d,f,h\} = \{a,b,c,d,e,f,g,h\}$

Step2: Find the complement $(A\cup B\cup C)'$

Subtract $A\cup B\cup C$ from universal set U:
$(A\cup B\cup C)' = U - (A\cup B\cup C) = \{a,b,c,d,e,f,g,h\} - \{a,b,c,d,e,f,g,h\}$

Answer:

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