Word Count : 495

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To apply quantification rules to prove the validity or invalidity of syllogistic arguments, we must express each argument in symbolic form using predicate logic and then apply logical rules like universal instantiation, existential instantiation, universal generalization, and rules of inference such as modus ponens and modus tollens. Let us evaluate a few examples of syllogistic arguments with appropriate use of quantification rules to determine their validity. Example 1: All humans are mortal. Socrates is a human. ∴ Socrates is mortal. Let: * H(x): x is a human * M(x): x is mortal * s: Socrates Symbolic Representation: 1. ∀x (H(x) → M(x)) 2. H(s) ∴ M(s) Proof: From (1), using Universal Instantiation: 3\. H(s) → M(s) From (2): 4\. H(s) Now apply Modus __________ ______ ___ ____ ____ _______ _________ ___.
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