Notations and Examples
| Component | Example | Notation |
| Propositions | "The Sky is blue." | P,Q,R, . . . |
| Logical Connectives | Conjunction (AND) | P ∧ Q |
| | Disjunction (OR) | P V Q |
| | Negation (NOT) | ~P |
| | Implication (IF-THEN) | P →Q |
| | Biconditional (IF AND ONLY IF) | P ↔Q |
| Truth Table |  | - |
| Logical Laws and Rules | De Morgan's Law 1: ¬(P ∧ Q) ≡ ¬P ∨ ¬Q | - |
| | De Morgan's Law 2: ¬(P ∨ Q) ≡ ¬P ∧ ¬Q | - |
| Validity | Premise1: "If it is raining, then... | - |
| | Premise 2: "It is raining." | - |
| | Conclusion: "Therefore, the ground..." | - |
| Predicate Logic | Universal Quantifier: For all x, P(x) | ∀x P(x) |
| | Existential Quantifier: There exists x... | ∃x P(x) |