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This 2 page Class Notes was uploaded by Kaitlyn Herbst on Monday March 9, 2015. The Class Notes belongs to Philos 1500 at Ohio State University taught by Peter Celello in Spring2015. Since its upload, it has received 93 views.
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Date Created: 03/09/15
Chap 75 Logically Signi cant Categories and Relationships 1500 Intro to Logic Vocab Tautology statement that is true on every assignment of truth values to its atomic components Contradiction statement that is false on every assignment of truth values to its atomic components Contingent statement that is true on some assignments of truth values to its atomic components and false on others Logically equivalent two statements that agree in truth value on every assignment of truth values to their atomic components Logically contradictory two statements that disagree in truth value on every assignment of truth values to their atomic components Logically consistent two or more statements that are all true on some assignment of truth values to their atomic components Logically inconsistent two or more statements that are never all true on any assignment of truth values to their atomic components Truth tables can be used to sort statements into Logically signi cant categories 0 Tautologies o Contradictions o Contingent statements Logically signi cant relationships 0 Equivalence o Contradictoriness 0 Consistency o Inconsistency Tautology Contradiction and Contingency How appear on a truth table Tautology true on every row Contradiction false on every row Contingency true on some rows false on others Equivalence Contradictoriness Consistency and Inconsistency How appear on a truth table Equivalence two statements have the same truth value on each row Contradictoriness two statements have a different truth value on each row Consistency two or more statements have the same truth value on at least one FOW Inconsistency two or more statements where there is no row where they are bothall true Relationships Every argument whose conclusion is a tautology is valid Any argument that includes a contradiction among its premises is valid Any argument with logically inconsistent premises is valid and unsound Any argument that has a tautology as its premise and a contingent statement as its conclusion is invalid If premises of an argument when made into a conjunction form a contingent statement and the conclusion is a contradiction the argument is invalid If a biconditional statement is a tautology then its two constituent statements are logically equivalent
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