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| title | TARGET DECK | FILE TAGS | tags | ||
|---|---|---|---|---|---|
| Additive Principle | Obsidian::STEM | combinatorics set |
|
Overview
The additive principle states that two finite and disjoint sets A and B satisfy |A \cup B| = |A| + |B|
This can be generalized to any number of finite and disjoint sets in the obvious way.
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Basic
What does the additive principle state?
Back: Given finite and disjoint sets A and B, |A \cup B| = |A| + |B|.
Reference: Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd ed., n.d., https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf.
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%%ANKI Basic The additive property applies to sets exhibiting what two properties? Back: Finiteness and disjointedness. Reference: Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd ed., n.d., https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf.
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Basic
Why does |A \cup B| \neq |A| + |B| in the general sense?
Back: Members of A \cap B are counted twice erroneously.
Reference: Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd ed., n.d., https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf.
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Basic
Which C construct corresponds to the additive property?
Back: union
Reference: Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd ed., n.d., https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf.
Tags: c17
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Basic
How do we denote A and B are disjoint using standard set notation?
Back: A \cap B = \varnothing
Reference: Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd ed., n.d., https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf.
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Bibliography
- Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd ed., n.d., https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf.