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TRUTH TABLES The general truth tables for each of the connectives tell you the value of any possible statement for each of the connectives. Negation ~ p F T

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**Conjunction (Asserts both statements are true.)**

p q T F

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**Disjunction (Asserts at least one statement is true.)**

p v q T F

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**Material Equivalence (Asserts the statements always have the same truth value.) **

p q T F

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**(Antecedent sufficient for consequent)**

Material Implication (Antecedent sufficient for consequent) One must assume that a material implication is true unless one can prove that it’s false. If you make a perfect score on all your work, then you make an A for the course. p q T F

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To determine how many lines a truth table will have use this formula: Lines = 2n n = the number of different letters (simple statements) in the statement. Starting with the left most letter, divide the table in half. Assign T as the value of the left most letter for the first half of the table, and F as its value for the second half of the table. Move to the next new letter to the right, and cut the alternation between T & F in half. Repeat this process until you are alternating between T& F line by line for the right most letter.

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**Tautology: A statement in which the form necessitates that it be true**

Tautology: A statement in which the form necessitates that it be true. It’s truth table has T on every line beneath its main symbol. Self-Contradiction: A statement in which the form necessitates that it be false. It’s truth table has F on every line beneath its main symbol. Contingent Statement: A statement in which the truth value is contingent upon the particular combination of values you have for its letters (simple statements). It’s truth table has T on some lines and F on some lines beneath its main symbol.

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Logically Equivalent Statements: The two statements have the same truth value on every line beneath their main symbols. Logically Contradictory Statements: The two statements have the opposite truth values on every line beneath their main symbols.

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**Consistent Statements: **

The statements are neither equivalent nor contradictory. There is at least one line on which both statements are true. Inconsistent Statements: There is not at least one line on which both statements are true.

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If there is no line on which all the premises are true and the conclusion false, then the argument is valid. If there is even one line on which all the premises are true and the conclusion false, then the argument is invalid.

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Section 3.2: Truth Tables for Negation, Conjunction, and Disjunction

Section 3.2: Truth Tables for Negation, Conjunction, and Disjunction

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