Difference between revisions of "Distributivity of intersections across unions"
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Latest revision as of 23:19, 18 August 2016
Stub grade: D
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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
Contents
Statement
- [ilmath]A\cap(B\cup C)=(A\cap B)\cup(A\cap C)[/ilmath]
- [ilmath]A\cap(\bigcup_{i=1}^n B_i)=\bigcup_{i=1}^n(A\cap B_i)[/ilmath] - Easy to do, use induction
Proof
Grade: C
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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
- Distributivity of unions across intersections (almost the same: [ilmath]A\cup(B\cap C)=(A\cup B)\cap(A\cup C)[/ilmath])
References