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

Combine all unique elements of $A$ and $B$:
$A\cup B = \{d,f,h\} \cup \{a,f,h\} = \{a,d,f,h\}$

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

Take elements in $U$ not in $A\cup B$:
$(A\cup B)' = U - (A\cup B) = \{a,b,c,d,e,f,g,h\} - \{a,d,f,h\} = \{b,c,e,g\}$

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

Find common elements of $(A\cup B)'$ and $C$:
$(A\cup B)'\cap C = \{b,c,e,g\} \cap \{a,b,c,e,g\} = \{b,c,e,g\}$

Answer:

A. $(A\cup B)'\cap C = \{b,c,e,g\}$