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title TARGET DECK FILE TAGS tags
Additive Principle Obsidian::STEM combinatorics set
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.

%%ANKI 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.

END%%

%%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.

END%%

%%ANKI 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.

END%%

%%ANKI 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: c

END%%

%%ANKI 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.

END%%

References