Module Complete
Predicate Logic — Quick Reference
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Completion
Quantifiers
| Symbol | Name | Truth Condition |
|---|---|---|
| ∀x | Universal (For all) | Every x satisfies the predicate |
| ∃x | Existential (There exists) | At least one x satisfies |
| ∃!x | Unique Existence | Exactly one x satisfies |
Negation Rules
¬(∀x P(x)) ≡ ∃x ¬P(x)
¬(∃x P(x)) ≡ ∀x ¬P(x)
SQL Equivalents
| Logic | SQL Pattern |
|---|---|
| ∃x P(x) | EXISTS (SELECT ... WHERE P) |
| ∀x P(x) | NOT EXISTS (... WHERE NOT P) |
Key Takeaways
1
∀ = all, ∃ = some
2
Quantifier ORDER matters: ∀x∃y ≠ ∃y∀x
3
Negating ∀ gives ∃¬, negating ∃ gives ∀¬
4
Universal in SQL = NOT EXISTS (counterexample)
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Module 5: Applications
Fallacies, puzzles, and real-world reasoning