is (A∩B)∩(B∩C)=B∩(A∩C) true | Mathematics | Page 1

mighty salmon Oct 22, 2024, 6:43 PM

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thats it.. i know this is probably really stupid but i just wanna make sure thanks in advance

lime glenBOT Oct 22, 2024, 6:43 PM

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digital solar Oct 22, 2024, 6:46 PM

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True

Take RHS
Bn(AnC)
(BnA)n(BnC)

mighty salmon Oct 22, 2024, 6:48 PM

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thanks a bunch

upper spruce Oct 22, 2024, 6:59 PM

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u can check by making venn diagram

gaunt niche Oct 22, 2024, 7:45 PM

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Yes, intersection is associative, so the brackets don't really matter much and taking a "double intersection" if you wish to call it like that (i.e. A∩B∩B = A∩B) doesn't do much.

#is (A∩B)∩(B∩C)=B∩(A∩C) true