Module Complete
Propositional Logic — Quick Reference
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Completion
Logical Connectives
| Symbol | Name | Truth Condition |
|---|---|---|
| ∧ | AND (Conjunction) | True only when BOTH are true |
| ∨ | OR (Disjunction) | True when AT LEAST ONE is true |
| ¬ | NOT (Negation) | Flips the truth value |
| → | IMPLIES (Conditional) | False only when T → F |
| ↔ | IFF (Biconditional) | True when both SAME value |
Key Equivalences
De Morgan's: ¬(P ∧ Q) ≡ ¬P ∨ ¬Q
De Morgan's: ¬(P ∨ Q) ≡ ¬P ∧ ¬Q
Implication: P → Q ≡ ¬P ∨ Q
Contrapositive: P → Q ≡ ¬Q → ¬P
Key Takeaways
1
Propositions have definite truth values (T or F)
2
AND requires both; OR requires at least one
3
Implication is only false for T → F
4
Use parentheses to clarify precedence
5
De Morgan's Laws help negate compound statements
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Module 2: Translation
Converting natural language to logical notation