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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
Today’s Topics
  • Symbolizing conditionals and bi-conditionals
  • Other complex symbolizations.
  • Unless
conditional
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
terms that precede the antecedent
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
terms that precede the consequent
Then

Only if

It follows that

Implies

Leads to

Means that

Is a sufficient condition for

Terms that Precede the Consequent
slide6
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
biconditional
Biconditional
  • A biconditional is composed of two elements
  • A biconditional is true when the elements agree in truth value (both true or both false)
biconditionals are introduced with the words if and only if or is necessary and sufficient for
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)

try some symbolizations
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
symbolizing neither nor and not both
Symbolizing “Neither Nor” and “Not Both”
  • We have two different ways to symbolize both ‘neither nor’ and ‘not both’.
demorgan s law 1 st version
DeMorgan’s Law (1st Version)
  • The negation of a disjunction is equivalent to a conjunction of the negations of the disjuncts.
demorgan s law 2 nd version
DeMorgan’s Law (2nd Version)
  • The negation of a conjunction is equivalent to a disjunction of the negations of the conjuncts
unless the word of the lorax
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!
key ideas
Key Ideas
  • Symbolizing conditionals
  • Other complex symbolizations
  • Unless