[table][tr][td][b]Component[/b][/td][td][b]Example[/b][/td][td][b]Notation[/b][/td][/tr][tr][td][/td][/tr][/table][size=150][table][tr][td]Propositions [/td][td]"The Sky is blue."[/td][td]P,Q,R, . . .[/td][/tr][tr][td]Logical Connectives [/td][td]Conjunction (AND) [/td][td]P ∧ Q[/td][/tr][tr][td][/td][td]Disjunction (OR)[/td][td]P V Q[/td][/tr][tr][td][/td][td]Negation (NOT)[/td][td]~P[/td][/tr][tr][td][/td][td][i]I[/i]mplication (IF-THEN)[/td][td]P →Q[/td][/tr][tr][td][/td][td]Biconditional[br](IF AND ONLY IF)[/td][td]P ↔Q[/td][/tr][tr][td]Truth Table[/td][td][img]data:image/png;base64,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[/img][/td][td]-[/td][/tr][tr][td]Logical Laws and Rules[/td][td]De Morgan's Law 1: ¬(P ∧ Q) ≡ ¬P ∨ ¬Q [/td][td]-[/td][/tr][tr][td][/td][td]De Morgan's Law 2: ¬(P ∨ Q) ≡ ¬P ∧ ¬Q[/td][td]-[/td][/tr][/table][br][table][tr][td]Validity [/td][td]Premise1: "If it is raining, then... [/td][td]- [/td][/tr][tr][td][/td][td]Premise 2: "It is raining."[/td][td]-[/td][/tr][tr][td][/td][td]Conclusion: "Therefore, the ground..."[br][/td][td]-[/td][/tr][tr][td]Predicate Logic[/td][td]Universal Quantifier: For all x, P(x)[/td][td]∀x P(x)[/td][/tr][tr][td][/td][td]Existential Quantifier: There exists x...[/td][td]∃x P(x)[/td][/tr][/table][/size][table][tr][td][/td][/tr][/table]