Predicates and Quantifiers
Predicates express properties or relationships whose truth depends on their inputs.
Summary
Predicates express properties or relationships whose truth depends on their inputs. A predicate becomes a proposition when its free variables receive values or are bound by quantifiers. Quantified statements depend on the predicate, the specified domain, and quantifier scope.
| Quantifier | Meaning | Evidence |
|---|---|---|
| Universal: | Every domain element satisfies the predicate | One counterexample refutes it |
| Existential: |
🧠 Key Concepts
- Predicates
- Universal Quantification
- Existential Quantification
- Free Variables
- Bound Variables
- Closed Formulas
- Quantifier Order
- Quantifier Negation
- Restricted Quantification
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Predicates and Quantifiers
📘 Overview Predicates describe properties or relationships whose truth depends on their inputs. Quantifiers turn these conditions into claims about all or some elements of a specified domain, forming the basis of precise software specifications and logical reasoning.
🧠 Key Idea A quantified statement is determined by its predicate, domain, and quantifier scope. Changing the domain or the order of different quantifiers can change the statement's truth.
⚔️ Core Details: - A predicate such as becomes a proposition when its free variables receive values or are bound by quantifiers. - Universal quantification,
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Part of 🌱 BSCS Year 1 — Computing & College Foundations
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