Difference between revisions of "Distributivity of intersections across unions"

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Latest revision as of 23:19, 18 August 2016

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Created for use with the ring of sets generated by a semi-ring is the set containing the semi-ring and all finite disjoint unions, the theorem is easy and routine, at least in the finite cases

Statement

  1. [ilmath]A\cap(B\cup C)=(A\cap B)\cup(A\cap C)[/ilmath]
  2. [ilmath]A\cap(\bigcup_{i=1}^n B_i)=\bigcup_{i=1}^n(A\cap B_i)[/ilmath] - Easy to do, use induction

Proof

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First one is routine chapter-1 for first-years, second one is easy using induction

This proof has been marked as an page requiring an easy proof

See also

References