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| title | TARGET DECK | FILE TAGS | tags | ||
|---|---|---|---|---|---|
| Combinatorics | Obsidian::STEM | combinatorics set |
|
Overview
The additive principle states that two finite and disjoint sets A and B satisfy |A \cup B| = |A| + |B|
The multiplicative principle states that two finite sets A and B satisfy |A \times B| = |A| \cdot |B|
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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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Basic
What does the multiplicative principle state?
Back: Given finite sets A and B, |A \times B| = |A| \cdot |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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%%ANKI Basic The multiplicative property applies to sets exhibiting what property? Back: Finiteness. Reference: Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd ed., n.d., https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf.
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Cloze
The additive principle is to {\cup} whereas the multiplicative principle is to {\times}.
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
If A is finite, how is A \times B rewritten as |A| disjoint sets?
Back: Given A = \{a_1, \ldots, a_n\}, (\{a_1\} \times B) \cup \cdots \cup (\{a_n\} \times 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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Basic
If B is finite, how is A \times B rewritten as |B| disjoint sets?
Back: Given B = \{b_1, \ldots, b_n\}, (A \times \{b_1\}) \cup \cdots \cup (A \times \{b_n\}).
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
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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Basic
How is the cartesian product A \times B defined?
Back: A \times B = \{\langle x, y \rangle : x \in A \land y \in 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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References
- Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd ed., n.d., https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf.