If A = 2, 3, 4, 8, 10 B = 3, 4, 5, 10, 12 and C = 4, 5, 6, 12, 14 then (A ∪ B) ∩ (A ∪ C)

Question

If A = 2, 3, 4, 8, 10 B = 3, 4, 5, 10, 12 and C = 4, 5, 6, 12, 14 then (A ∪ B) ∩ (A ∪ C) (A)  2, 3, 4, 5, 10, 12  (B)  2, 4, 10, 12  (C)  3, 8, 10, 12  (D)  2,8,10

Tardigrade Admin · Accepted Answer

(A ∪ B) ∩ (A ∪ C) = A ∪ (B ∩ C) = 2, 3, 4, 8, 10 ∪ 4, 5, 12 = 2, 3, 4, 5, 8, 10, 12

Q. If $A = {2, 3, 4, 8, 10}$ , $B = {3, 4, 5, 10, 12}$ and
$C = {4, 5, 6, 12, 14}$ , then $(A \cup B) \cap (A \cup C)$

${2, 3, 4, 5, 10, 12}$

${2, 4, 10, 12}$

${3, 8, 10, 12}$

${2, 8, 10}$

$(A \cup B) \cap (A \cup C) = A \cup (B \cap C)$
$= {2, 3, 4, 8, 10} \cup {4, 5, 12}$
$= {2, 3, 4, 5, 8, 10, 12}$

Q. If A={2,3,4,8,10}, B={3,4,5,10,12} and C={4,5,6,12,14}, then (A∪B)∩(A∪C)

{2,3,4,5,10,12}

{2,4,10,12}

{3,8,10,12}

{2,8,10}