2 Matching Annotations
- Feb 2021
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math.libretexts.org math.libretexts.org
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π΅βͺ(βπβπΌπ΄π)=βπβπΌπ΅βͺπ΄πBβͺ(βiβIAi)=βiβIBβͺAiB \cup\left(\bigcap_{i \in I} A_{i}\right)=\bigcap_{i \in I} B \cup A_{i};
Here's a simpler (hopefully similarly rigorous) proof I made for 1.1.3.a.
$$\bigcup_{i \in I}A_{i} \cup B =(B \cup A_{1}) \cap (B \cup A_{2}) \cap ... \cap(B \cup A_{i})$$
because distributive property of union over intersection $$= B \cup (A{1} \cap A{2}\cap ... \cap A_{i})$$
$$= B \cup (\bigcap_{i \in I}A_{i})$$
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detain
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