Chapter 6.3 Notes PDF

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Chapter 6.3 Notes Fall 2018...

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6.3 Truth Tables for Propositions ●

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A truth table presents all possible combinations of truth value assignments to the simple (atomic) propositions, and determines the truth value of the target compound proposition for each of such possible combinations (extension of other truth tables) ○ Lots of examples (in class exercises) in notebook ○ Longer version of other truth tables ■ Memorize bby truth tables to make these easier Creating truth tables for propositions can be useful for at least three reasons ○ Truth tables can be used to evaluate arguments (next section) ○ A truth table for a proposition shows a logical property of the proposition: tautology, self-contradiction, or contingent ○ A logical relationship between two propositions can be determined by comparing their truth tables Tautologous statement ○ Always true regardless of the truth value of its components Self-contradictory statement ○ Always false regardless of the truth values of the components Contingent statement ○ True or false, depending on the truth value of its components Logical relations between two statements can be determined by truth tables ○ Logically equivalent ■ They have the same truth value on each line (i.e. they have the same truth value under the same truth value assignments to its components) ○ Contradictory ■ They have the opposite truth values on each line ○ Inconsistent ■ There is no line on which both of them are true (i.e. there is no truth value assigment to the components that can make both statements true) ○ Consistent ■ There is at least one line on which both of them are true ● Logically equivalent statements are consistent (but the converse is not generally true) ● Contradictory statements are inconsistent (but the converse is not generally true)...