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Determine if valid or invalid. Using Rules of Inference. 25. If I don’t tie my shoes, then I trip. I didn’t tie my shoes. Hence, I tripped.

Determine if valid or invalid. Using Rules of Inference. 25. If I don’t tie my shoes, then I trip. I didn’t tie my shoes. Hence, I tripped.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Determine if valid or invalid. Using Rules of Inference.

25. If I don’t tie my shoes, then I trip. I didn’t tie my shoes. Hence, I tripped.

Symbols Names Rule Given a statement, it is permissible to infer any disjunction having that statement as one disjunct. 1. Addition ..P VQ Rules of PAQ PAQ 2. Q or P Simplification Simplification either of its conjuncts separately. Inference ..P ..Q Given two statements, it is permissible to infer the conjunction having them as conjuncts. 3. Q Conjunction ..PAQ P- Q Given a conditional, and given the antecedent of 4. P Modus Ponens that same conditional, it is permissible to infer the consequent of the same conditional. P. Given a conditional, and given the NEGATION of its CONSEQUENT, it is permissible to infer the NEGATION of its antecedent. Given two conditionals such that the consequent of one matches the antecedent of the other, it is permissible to infer a conditional having the UNMATCHED antecedent and the UNMATCHED 5. Modus Tollens P - Q Hypothetical Syllogism (Transitivity) Q-R 6. .. P-R consequent. P VQ PVQ Disjunctive Sylogism (Cancellation) disjuncts. Given a disjunction, and given the denial of one of its disjuncts, it is permissible to infer the other 7. -P or -Q ..Q .P P - Q Given two conditionals (or a conjunction of two conditionals) and given the disjunction of their antecedents, it is permissible to infer the disjunction of their consequents. 8. PVR Constructive Dilemma .QVS P - Q R -S 9. -QV-S Destructive Dilemma ..-P V -R P+Q P+Q Given a biconditional, and given one side of that same, biconditional, it is permissible to infer the other side of that biconditional. 10. Р or Q Equivalence .Q P Given a statement, it is permissible to infer that the Repetition 11. ..P P → Q 12. ..Р—(РЛQ) same statement. Absorption
Transcribed Image Text:Symbols Names Rule Given a statement, it is permissible to infer any disjunction having that statement as one disjunct. 1. Addition ..P VQ Rules of PAQ PAQ 2. Q or P Simplification Simplification either of its conjuncts separately. Inference ..P ..Q Given two statements, it is permissible to infer the conjunction having them as conjuncts. 3. Q Conjunction ..PAQ P- Q Given a conditional, and given the antecedent of 4. P Modus Ponens that same conditional, it is permissible to infer the consequent of the same conditional. P. Given a conditional, and given the NEGATION of its CONSEQUENT, it is permissible to infer the NEGATION of its antecedent. Given two conditionals such that the consequent of one matches the antecedent of the other, it is permissible to infer a conditional having the UNMATCHED antecedent and the UNMATCHED 5. Modus Tollens P - Q Hypothetical Syllogism (Transitivity) Q-R 6. .. P-R consequent. P VQ PVQ Disjunctive Sylogism (Cancellation) disjuncts. Given a disjunction, and given the denial of one of its disjuncts, it is permissible to infer the other 7. -P or -Q ..Q .P P - Q Given two conditionals (or a conjunction of two conditionals) and given the disjunction of their antecedents, it is permissible to infer the disjunction of their consequents. 8. PVR Constructive Dilemma .QVS P - Q R -S 9. -QV-S Destructive Dilemma ..-P V -R P+Q P+Q Given a biconditional, and given one side of that same, biconditional, it is permissible to infer the other side of that biconditional. 10. Р or Q Equivalence .Q P Given a statement, it is permissible to infer that the Repetition 11. ..P P → Q 12. ..Р—(РЛQ) same statement. Absorption
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