Use a standard form from Table 5.15or Table 5.16 to determine whether the following arguments are valid or invalid.a. If I go to Florida for spring break, then I will not study.I did not go to Florida for spring break.∴ I studied.b. If you helped solve the crime, then you should be rewarded.You helped solve the crime.∴ You should be rewarded. is valid. This symbolic form is known as direct reasoning. All arguments that have this symbolic fom are valid.Table 5.15 shows four symbolic forms and the name used to identify each form. Any argument that has a symbolicform identical to one of these symbolic forms is a valid argument.Table 5.15Standard Forms of Four Valid ArgumentsDirect ReasoningContrapositive Reasoning Transitive ReasoningDisjunctive ReasoningpVqpVqTransitive reasoning can be extended to include more than two conditional premises. For instance, if the conditionalpremises of an argument are p - q. q r, and r- s, then a valid conclusion for the argument is p → s.In example 4 we use standard forms to determine a valid conclusion for an argument.Example 4: Determine a Valid Conclusion for an ArgumentUse a standard form from Table 5.15 to determine a valid conclusion for each argument.a. If Kim is a lawyer (p), then she will be able to help us (q).Kim is not able to help us (~q).IIb. If they had a good time (g), they will return (r).If they return (r), we will make more money (m). Table 5.26 shows two symbolic forms associated with invalid arguments. Any argument that has one of thesesymbolic forms is invalid.Table 5.26Standard Forms of Two Invalid ArgumentsDirect Reasoning Contrapositive ReasoningExample 5: Use a Standard Form to Determine the Validity of an ArgumentUse a standard form from Table 5.15 or Table 5.16 to determine whether the following arguments are valid or invalid.a. The program is interesting or I will watch the basketball game.The program is not interesting.:I will watch the basketball game.b. IfI have a cold, then I find it difficult to sleep.I find it difficult to sleep.AI have a cold.II

determine whether the following arguments are valid or invalid. a. If I go to Florida for spring break, then I will not study.I did not go to Florida for spring break.∴ I studied. b. If you helped solve the crime, then you should be rewarded.You helped solve the crime.∴ You should be rewarded. a) let if i go to florida for spring break be denoted by f i will not study be s we can write, If I go to Florida for spring break, then I will not study as f→s I did not go to Florida for spring break. ¬f combining both the statements, we get ¬s that is, i will study f s f→s ¬f ¬s T T T F F T F F F T F T T T critical rows F F F T T critical rows T since the conclusion is not true in all critical rows , hence the statement is not valid b) If you helped solve the crime, then you should be rewarded.You helped solve the crime.∴ You should be rewarded. let, If you helped solve the crime be denoted by p you should be rewarded by q we can write, If you helped solve the crime, then you should be rewarded as p→q You helped solve the crime. p therefore, You should be rewarded using modus ponens , we get q hence it is valid

Math

Advanced Math

Use a standard form from Table 5.15or Table 5.16 to determine whether the following arguments are valid or invalid. a. If I go to Florida for spring break, then I will not study. I did not go to Florida for spring break. ∴ I studied. b. If you helped solve the crime, then you should be rewarded. You helped solve the crime. ∴ You should be rewarded.

Use a standard form from Table 5.15or Table 5.16 to determine whether the following arguments are valid or invalid. a. If I go to Florida for spring break, then I will not study. I did not go to Florida for spring break. ∴ I studied. b. If you helped solve the crime, then you should be rewarded. You helped solve the crime. ∴ You should be rewarded.

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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