Question

let sets a, b, and c be subsets of u, where: a = {a, c, d, f, h} b = {a, b, d, e, f, h, i} c = {a, c, e, g} complete a venn diagram for the sets and then answer the question following. list the elements in the set (a ∩ c) ∪ (b ∩ a) { } enter the elements as a list, separated by commas. if the result is the empty set, enter dne

Explanation:

Step1: Find $A \cap C$

$A \cap C = \{a, c\}$

Step2: Find $(A \cap C)'$

Elements in $U$ (all given elements) not in $A \cap C$:
$(A \cap C)' = \{b, d, e, f, g, h, i\}$

Step3: Find $B \cap A$

$B \cap A = \{a, d, f, h\}$

Step4: Find $(B \cap A)'$

Elements in $U$ not in $B \cap A$:
$(B \cap A)' = \{b, c, e, g, i\}$

Step5: Find union of the two sets

Combine unique elements from $(A \cap C)'$ and $(B \cap A)'$:
$\{b, d, e, f, g, h, i\} \cup \{b, c, e, g, i\} = \{b, c, d, e, f, g, h, i\}$

Answer:

b, c, d, e, f, g, h, i