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Propositional Logic

Propositional Logic. Propositional Logic. A proposition is a statement that is either true or false. We give propositions names such as p , q , and r . E.g. p = “pigs have wings” q = “Obama is U.S. president” In this world anyway, p is false and q is true. Truth Tables. −.

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Propositional Logic

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  1. Propositional Logic

  2. Propositional Logic A proposition is a statement that is either true or false. We give propositions names such as p, q, and r. E.g. p = “pigs have wings” q = “Obama is U.S. president” In this world anyway, p is false and q is true.

  3. Truth Tables − • “Not” • ¬p is also written p

  4. Logical Operators/Connectives Building propositions from propositions “And” So “pigs have wings and Obama is US president” …

  5. Logical Operators/Connectives “Or” So “pigs have wings or Obama is US president” … “Or” is ambiguous in English but not in Propositional Logic E.g., “would you like coffee or ice cream?”

  6. Logical Operators/Connectives • “Exclusive or”

  7. Some expressions can be defined in terms of others • p ⊕ q is equivalent to (p∨q) ∧¬(p∧q) • What does this actually mean? • That the truth value of the formula on the left is the same as the truth value of the formula on the right regardless of the truth values of p and q

  8. Propositional Logic

  9. Implies p ⇒q or p→q or p⊃q is equivalent to ¬p∨q So “If pigs have wings then Obama is US president” is true in this world In fact a false proposition implies any proposition

  10. “Iff” or logical equivalence p ⇔ q means that p and q have the same truth value Equivalent to (p ⇒ q) ∧ (q ⇒ p)

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