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Question
Verify the associative property of intersection of sets for A = `{-11, sqrt(2), sqrt(5), 7}`, B = `{sqrt(3), sqrt(5), 6, 13}` and C = `{sqrt(2), sqrt(3), sqrt(5), 9}`
Solution
Associative Property of intersection of sets A ∩ (B ∩ C) = (A ∩ B) ∩ C
B ∩ C = `{sqrt(3), sqrt(5), 6, 13} ∩ {sqrt(2), sqrt(3), sqrt(5), 9} = {sqrt(3), sqrt(5)}`
A ∩ (B ∩ C) = `{-11, sqrt(2), sqrt(5), 7} ∩ {sqrt(3), sqrt(5)} = {sqrt(5)}` ...(1)
A ∩ B = `{-11, sqrt(2), sqrt(5), 7} ∩ {sqrt(3), sqrt(5), 6, 13} = {sqrt(5)}`
(A ∩ B) ∩ C = `{sqrt(5)} ∩ {sqrt(2), sqrt(3), sqrt(5), 9} = {sqrt(5)}` ...(2)
From (1) and (2),
It is verified that A ∩ (B ∩ C) = (A ∩ B) ∩ C
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