Today's Topics - Southeast Missouri State University

Today’s Topics
Symbolizing conditionals and bi-conditionalsOther complex symbolizations.Unless
Conditional
Aconditionalis composed of two elements, theantecedent(the ‘if’ part of an if, then, statement) and theconsequent(the ‘then’ part)A conditional is true if either the antecedent is false or the consequent true
MANTRA: A Conditional With a False Antecedent Is True
Terms that Precede the Antecedent
IfGiven thatInsofar asProvided thatSo long asIn caseFollows from
Is implied byWheneverIs a necessary condition for
Terms that Precede the Consequent
ThenOnly ifIt follows thatImpliesLeads toMeans that
Is a sufficient condition for
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 QPQP is a necessary condition for QQ P
Biconditional
Abiconditionalis composed of two elementsA 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”
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
Download theHandoutlabeled Conditional Study Guide and attempt the exercisesPost some of your answers to the bulletin boards and discuss them
Symbolizing “Neither Nor” and “Not Both”
We have two different ways to symbolize both ‘neither nor’ and ‘not both’.
Two Ways to Symbolize “Neither P nor Q”
~(PvQ)(~P~Q)
DeMorgan’s Law (1stVersion)
The negation of a disjunction is equivalent to a conjunction of the negations of the disjuncts.
Two Ways to Symbolize “Not Both”
~(PQ)(~Pv ~Q)
DeMorgan’s Law (2ndVersion)
The negation of a conjunction is equivalent to a disjunction of the negations of the conjuncts
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 theHandouton Unless and see what havoc this word can wreak!
Key Ideas
Symbolizing conditionalsOther complex symbolizationsUnless