4.5 KiB
| title | TARGET DECK | FILE TAGS | tags | ||
|---|---|---|---|---|---|
| Quantification | Obsidian::STEM | logic::quantification |
|
Overview
- Existential quantification asserts the existence of a member in a set (denoted the range) satisfying a property. There may be multiple members that satisfy the property; so long as one does, the existential quantification is considered true.
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Basic
What symbol denotes existential quantification?
Back: \exists
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
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%%ANKI Basic How many members must satisfy a property in existential quantification? Back: At least one. Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
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Basic
\exists x : S, P(x) is shorthand for what?
Back: \exists x, x \in S \land P(x)
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
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Basic
What is the identity element of \lor?
Back: F
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
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- Universal quantification asserts that every member of a set satisfies a property.
%%ANKI
Basic
What symbol denotes universal quantification?
Back: \forall
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
%%ANKI Basic How many members must satisfy a property in universal quantification? Back: All of them. Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
%%ANKI
Basic
\forall x : S, P(x) is shorthand for what?
Back: \forall x, x \in S \Rightarrow P(x)
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
%%ANKI
Basic
What is the identity element of \land?
Back: T
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
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Cloze
{1:\exists} is to {2:\lor} as {2:\forall} is to {1:\land}.
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
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Basic
How is \forall x : S, P(x) equivalently written in terms of existential quantification?
Back: \neg \exists x : S, \neg P(x)
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
%%ANKI
How is \exists x : S, P(x) equivalently written in terms of universal quantification?
Back: \neg \forall x : S, \neg P(x)
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
- Counting quantification asserts that a number of members of a set satisfy a property.
%%ANKI
Basic
What symbol denotes counting quantification (of exactly k members)?
Back: \exists^{=k}
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
%%ANKI
Basic
What symbol denotes counting quantification (of at least k members)?
Back: \exists^{\geq k}
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
%%ANKI
Basic
How is \exists x : S, P(x) written in terms of counting quantification?
Back: \exists^{\geq 1} x : S, P(x)
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
%%ANKI
Basic
How is \forall x : S, P(x) written in terms of counting quantification?
Back: Assuming S has k members, \exists^{= k} x : S, P(x)
Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
END%%
Reference
- Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.