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Question
Given A = {0, 1, 2, 4, 5}, B = {0, 2, 4, 6, 8} and C = {0, 3, 6, 9}. Show that A ∩ (B ∩ C) = (A ∩ B) ∩ C i.e. the intersection of sets is associative.
Solution
B ∩ C = {0, 2, 4, 6, 8} ∩ {0, 3, 6, 9}
= {0,6}
Now, A ∩ (B ∩ C) = {0, 1, 2, 4, 5} ∩ {0,6}
⇒ A ∩ (B ∩ C) = {0} ...(I)
A ∩ B = {0, 1, 2, 4, 5} ∩ {0, 2, 4, 6, 8}
= {0,2,4}
∴ (A ∩ B) ∩ C = {0,2,4} ∩ {0, 3, 6, 9}
⇒ (A ∩ B) ∩ C = {0} ...(II)
From I and II we get
A ∩ (B ∩ C) = (A ∩ B) ∩ C
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