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Section 8.3

# Section 8.3 - case that the antecedent is true and the...

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Section 8.3 Conditional statements in English: Compound proposition Takes if-then form ‘If Ben like ice cream, then Jerry likes cupcakes’ Antecedent: Ben likes ice cream Consequent: Jerry likes cupcakes Logical: If all GW students are mortal, and you’re a GW student, then you are mortal o Logical between antecedent and consequent Definitional: ‘If that guy is unmarried, then he is a bachelor’ o Useful for clarifying meanings of certain concepts o ‘If that guy is a bachelor, then he’s unmarried’ relation expressed definitional Causal: ‘If there is lightning, then it will thunder’ Decisional: ‘If I go to the store, then I am buying orange juice’ o Practical decision making Material implication- If the conditional is true, then it cannot be the

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Unformatted text preview: case that the antecedent is true and the consequent is false (applies to all forms) • If P then Q, can use arrow or horseshoe A –> B Method 1: o Ask: is the consequent true? o Statement has to be true o If not, determine whether the antecedent is true or false Method 2: o Ask: is the antecedent false? o If so, then the statement is true o If not, then determine the truth value of the consequent P Q P –> Q ~(P • ~Q) T T T T T F F F F T T T F F T T (A –> B) –> Z T T F True antecedent, false consequent, FALSE STATEMENT {[(X –> Y) –> Z] –> [Z –> (X –> Y)]} -> [(X -> Z) -> Y] (F -> T) -> F T -> F F [P -> (Q->P)] -> Y Experiment w/ true and false values for unknowns Statement is False...
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Section 8.3 - case that the antecedent is true and the...

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