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Today’s Topics

Today’s Topics. Symbolizing conditionals and bi-conditionals Other complex symbolizations. Unless. Conditional. A conditional is composed of two elements, the antecedent (the ‘if’ part of an if, then, statement) and the consequent (the ‘then’ part)

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Today’s Topics

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  1. Today’s Topics • Symbolizing conditionals and bi-conditionals • Other complex symbolizations. • Unless

  2. Conditional • A conditional is composed of two elements, the antecedent (the ‘if’ part of an if, then, statement) and the consequent (the ‘then’ part) • A conditional is true if either the antecedent is false or the consequent true

  3. MANTRA: A Conditional With a False Antecedent Is True

  4. If Given that Insofar as Provided that So long as In case Follows from Is implied by Whenever Is a necessary condition for Terms that Precede the Antecedent

  5. Then Only if It follows that Implies Leads to Means that Is a sufficient condition for Terms that Precede the Consequent

  6. The language of necessary and sufficient conditions is the language of conditionals. • Sufficient conditions are antecedents of conditionals. Necessary conditions are consequents of conditionals. • P is a sufficient condition for Q • P  Q • P is a necessary condition for Q • Q  P

  7. Biconditional • A biconditional is composed of two elements • A biconditional is true when the elements agree in truth value (both true or both false)

  8. Biconditionals are introduced with the words “if and only if” or “is necessary and sufficient for” P is both necessary and sufficient for Q (P is necessary for Q) AND (P is sufficient for Q) (Q  P) & (P  Q) (P if Q) and (P only if Q) P Q (P if and only if Q)

  9. Try some symbolizations • Download the Handout labeled Conditional Study Guide and attempt the exercises • Post some of your answers to the bulletin boards and discuss them

  10. Symbolizing “Neither Nor” and “Not Both” • We have two different ways to symbolize both ‘neither nor’ and ‘not both’.

  11. Two Ways to Symbolize “Neither P nor Q” • ~(P v Q) • (~P  ~Q)

  12. DeMorgan’s Law (1st Version) • The negation of a disjunction is equivalent to a conjunction of the negations of the disjuncts.

  13. Two Ways to Symbolize “Not Both” • ~(P  Q) • (~P v ~Q)

  14. DeMorgan’s Law (2nd Version) • The negation of a conjunction is equivalent to a disjunction of the negations of the conjuncts

  15. UNLESS (the word of the Lorax!) • For a logician, unless means ‘or.’ And ‘or’ is inclusive unless otherwise specified. • Yes, this use of ‘unless’ violates our common use, but logic is a normative discipline and often the logician wishes to reform ordinary use. • When you see ‘unless’ in a sentence, replace it with a wedge! You can’t go wrong doing that. • Download the Handout on Unless and see what havoc this word can wreak!

  16. Key Ideas • Symbolizing conditionals • Other complex symbolizations • Unless

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