AdditionRULES OF INFERENCESimplificationConjunctionAbsorptionModus PonensModus TollensDisjunctiveSyllogismHypotheticalSyllogismConstructiveDilemmaDestructiveDilemmaDecomposing aConjunctionPAPVQPAQ or PAQ& PP4&P- (PAQ)P+QPvQ-PP+QQ-RAP-RPAQ(P+Q) ^ (RPVRS)Qvs(PQ) A (R <-S)V-S& PV-RPAQP C. Rules of InferenceDirection: Prove the validity of the following arguments.1. If it rains tonight, Payne will eat his snacks and does not need to water theplants. If Payne eats his snacks, then he is full. Payne is not full. Therefore, itdoes not rain tonight. Use P, Q, R, and S to represent the propositions.2. Prove the validity of the argument with the following premise and conclusion:Premise 1: P→ QPremise 2: -QA (R V~Q)Conclusion: ~(PAQ)

1. Suppose, P="It rains tonight." Q="Payne will eat his snacks." R="He is full." S="He needs to…

Answered: C. Rules of Inference Direction: Prove…

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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Prove the following argument by contradiction. See the example below for reference. Use the rules of equvalence and inference for justification.
b) Consider the arguments below: Amin doesn't like mathematics or he attends the classes. If Amin attends the classes or study hard, then he will pass the examination. Amin failed the exam. i) Using variables p, q, r and s, write down the primary statements ii) Write the premises using variables in (i) iii) Find the conclusion of the arguments by using the rules of inference.
QUESTION 3 Identify the form of the conditional argument and determine its validity: Premise: If you make bread, then you must use an oven. Premise: Jessica used an oven. Conclusion: Jessica baked bread. Affirming the hypothesis; valid Affirming the conclusion: not valid Denying the hypothesis; not valid O Denying the conclusion: valid
Use the first thirteen rules of inference to derive the conclusions of the symbolized argument below. AFLU W X MP Dist 1 2 3 4 MT DN HS Trans PREMISE A. (FL) PREMISE A (U V W) PREMISE F (U V X) PREMISE ( ) DS Impl { CD Equiv CONCLUSION U V (W. X) } [ ] Simp Exp Conj Add Taut ACP DM CP Com AIP Assoc IP
Which of the symbolic form represents the hypothesis
Use the first thirteen rules of inference to derive the conclusion of the symbolized argument below. HKL 3 C • כ V ( ) { } [ MP MT HS DS CD Simp Conj Add DM Com Assoc Dist DN Trans Impl Equiv Exp Taut ACP CP AIP IP PREMISE 1 (K • H) v (K • L) PREMISE 2 -L 3 PREMISE CONCLUSION H
Use the eighteen rules of inference to derive the conclusions of the symbolized argument below. B D M 2 MP Dist 1 2 3 D V = ( ) { } [ HS DS CD Simp Conj Trans Impl Equiv Exp Taut MT DN PREMISE (BM) (DM) PREMISE B v D PREMISE 1 CONCLUSION M Add ACP DM CP Com AIP Assoc IP
Consider the construction of a vending machine's logic. Assume that every soda costs a quarter, and that the machine accepts only quarters. E = True indicates the machine is empty, it has no more sodas S = True indicates the user has made a selection P = True indicates the user has paid a quarter The machine may send two control commands to its machinery: V = True indicates machine will give the user a soda (i.e. "vend") R = True indicates machine will return the user's quarter The machine should return a user's quarter only when they have paid and the machine is empty. The machine should give a soda only when a user has paid, made a selection and the machine is not empty.
2. Let p, q, and r be propositions. Show that the following argument is valid by using rules of inference. Show every step used and write down the justification for each. pv q ¬р 1¬р q^¬r
Use the method of writing each premise in symbols in order to write a conclusion that yields a valid argument. Hard workers sweat Sweat brings on a chill. Anyone who doesn't have a cold never felt a chill. Anyone who works doesn't have a cold. OA. Hard workers don't get colds. O B. Hard workers don't go to work. OC. Anyone who sweats works hard. O D. Anyone who has a cold works hard.

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