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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
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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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 symbolic form identical to one of these symbolic forms is a valid argument. Table 5.15 Standard Forms of Four Valid Arguments Direct Reasoning Contrapositive Reasoning Transitive Reasoning Disjunctive Reasoning pVq pVq Transitive reasoning can be extended to include more than two conditional premises. For instance, if the conditional premises 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 Argument Use 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). II b. If they had a good time (g), they will return (r). If they return (r), we will make more money (m).
Transcribed Image Text: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 symbolic form identical to one of these symbolic forms is a valid argument. Table 5.15 Standard Forms of Four Valid Arguments Direct Reasoning Contrapositive Reasoning Transitive Reasoning Disjunctive Reasoning pVq pVq Transitive reasoning can be extended to include more than two conditional premises. For instance, if the conditional premises 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 Argument Use 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). II b. 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 these symbolic forms is invalid. Table 5.26 Standard Forms of Two Invalid Arguments Direct Reasoning Contrapositive Reasoning Example 5: Use a Standard Form to Determine the Validity of an Argument Use 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
Transcribed Image Text:Table 5.26 shows two symbolic forms associated with invalid arguments. Any argument that has one of these symbolic forms is invalid. Table 5.26 Standard Forms of Two Invalid Arguments Direct Reasoning Contrapositive Reasoning Example 5: Use a Standard Form to Determine the Validity of an Argument Use 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
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