Publish on 17th November 2019
Category: Birds
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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 QPQP 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) & (PQ)(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”

~(PQ)(~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

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Today's Topics - Southeast Missouri State University