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Question
If A = {p, q, r, s}, B = {m, n, q, s, t} and C = {m, n, p, q, s}, then verify the associative property of union of sets
Solution
Associative Property of union of sets
A ∪ (B ∪ C) = (A ∪ B) ∪ C
(B ∪ C) = {m, n, q, s, t} ∪ {m, n, p, q, s}
= {m, n, p, q, s, t}
A ∪ (B ∪ C) = {p, q, r, s} ∪ {m, n, p, q, s, t}
= {m, n, p, q, r, s, t} ...(1)
(A ∪ B) = {p, q, r, s} ∪ {m, n, q, s, t}
= {m, n, p, q, r, s, t}
(A ∪ B) ∪ C = {m, n, p, q, r, s, t} ∪ {m, n, p, q, s}
= {m, n, p, q, r, s, t} ...(2)
From (1) and (2)
It is verified that A ∪ (B ∪ C) = (A ∪ B) ∪ C
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