59 lines
2.3 KiB
Markdown
59 lines
2.3 KiB
Markdown
---
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title: Additive Principle
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TARGET DECK: Obsidian::STEM
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FILE TAGS: combinatorics set
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tags:
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- combinatorics
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- set
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---
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## Overview
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The **additive principle** states that two finite and disjoint sets $A$ and $B$ satisfy $$|A \cup B| = |A| + |B|$$
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This can be generalized to any number of finite and disjoint sets in the obvious way.
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%%ANKI
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Basic
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What does the additive principle state?
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Back: Given finite and disjoint sets $A$ and $B$, $|A \cup B| = |A| + |B|$.
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Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
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<!--ID: 1708217738464-->
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END%%
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%%ANKI
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Basic
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The additive property applies to sets exhibiting what two properties?
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Back: Finiteness and disjointedness.
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Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
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<!--ID: 1708217738473-->
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END%%
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%%ANKI
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Basic
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Why does $|A \cup B| \neq |A| + |B|$ in the general sense?
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Back: Members of $A \cap B$ are counted twice erroneously.
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Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
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<!--ID: 1708346613616-->
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END%%
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%%ANKI
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Basic
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Which C construct corresponds to the additive property?
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Back: `union`
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Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
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Tags: c
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<!--ID: 1708221293486-->
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END%%
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%%ANKI
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Basic
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How do we denote $A$ and $B$ are disjoint using standard set notation?
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Back: $A \cap B = \varnothing$
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Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
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<!--ID: 1708217738491-->
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END%%
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## References
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* Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf). |