Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
LEARNING ACTIVITY 4.3 In exercises 1-6, determine whether the argument is valid or invalid by comparing its symbolic form into standard forms. For each valid argument, state the name of its standard form. 1. If you take Art 151 in the fall, you will be eligible to take Art 151 in the spring. You were not eligible to take Art 152 in the spring. Therefore, you did not take Art 151 in the fall.

LEARNING ACTIVITY 4.3 In exercises 1-6, determine whether the argument is valid or invalid by comparing its symbolic form into standard forms. For each valid argument, state the name of its standard form. 1. If you take Art 151 in the fall, you will be eligible to take Art 151 in the spring. You were not eligible to take Art 152 in the spring. Therefore, you did not take Art 151 in the fall.

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
See similar textbooks
icon
Related questions
Question
Important note: please make solutions TYPEWRITTEN and NOT HANDWRITTEN Use the given lesson attached as reference
STANDARD FORMS Arguments can be shown to be valid if they have the same symbolic form as an argument that is known to be valid. For instance, we have shown that the argument h-m h am is valid. This symbolic form is known as direct reasoning. All arguments that have this symbolic form are valid. Table 4.1 Standard Form of Four (4) Valid Arguments Direct Reasoning p-q P Aq Contrapositive Reasoning p-q -9 p-q -9 -p Transitive Reasoning Disjunctive Reasoning g-r r-m Note that transitive reasoning can be extended more than two (2) conditional premises. Say, if we have p→q, q→r, and r→s then a valid conclusion for the arguments is p→s. Example 4.3 Use standard form to determine a valid conclusion for the following arguments. 1. If Kim is a lawyer (p), then she will be able to help us (q). Kim is not able to help us (-p). Therefore: Solution: The symbolic form of the premises is If they had a good time (g), they will return (r). If they return (r), we will make more money (m). Therefore: p-q Solution: The symbolic form for the premises is q-r -p-r This matches the standard form known as contrapositive reasoning. Thus the valid conclusion is -p (Kim is not a lawyer.) p-q q AP p pvq -P Aq Table 4.2 Standard Form of Two (2) Invalid Arguments On the other hand, this matches the standard form called transitive reasoning thus, the valid conclusion is gm (If they had a good time, they will make more money). Fallacy of the Converse Fallacy of the Inverse pvq -q -p p-q P Any argument that matches either of the two forms as illustrated is invalid.
Transcribed Image Text:STANDARD FORMS Arguments can be shown to be valid if they have the same symbolic form as an argument that is known to be valid. For instance, we have shown that the argument h-m h am is valid. This symbolic form is known as direct reasoning. All arguments that have this symbolic form are valid. Table 4.1 Standard Form of Four (4) Valid Arguments Direct Reasoning p-q P Aq Contrapositive Reasoning p-q -9 p-q -9 -p Transitive Reasoning Disjunctive Reasoning g-r r-m Note that transitive reasoning can be extended more than two (2) conditional premises. Say, if we have p→q, q→r, and r→s then a valid conclusion for the arguments is p→s. Example 4.3 Use standard form to determine a valid conclusion for the following arguments. 1. If Kim is a lawyer (p), then she will be able to help us (q). Kim is not able to help us (-p). Therefore: Solution: The symbolic form of the premises is If they had a good time (g), they will return (r). If they return (r), we will make more money (m). Therefore: p-q Solution: The symbolic form for the premises is q-r -p-r This matches the standard form known as contrapositive reasoning. Thus the valid conclusion is -p (Kim is not a lawyer.) p-q q AP p pvq -P Aq Table 4.2 Standard Form of Two (2) Invalid Arguments On the other hand, this matches the standard form called transitive reasoning thus, the valid conclusion is gm (If they had a good time, they will make more money). Fallacy of the Converse Fallacy of the Inverse pvq -q -p p-q P Any argument that matches either of the two forms as illustrated is invalid.
LEARNING ACTIVITY 4.3 In exercises 1-6, determine whether the argument is valid or invalid by comparing its symbolic form into standard forms. For each valid argument, state the name of its standard form. 1. If you take Art 151 in the fall, you will be eligible to take Art 151 in the spring. You were not eligible to take Art 152 in the spring. Therefore, you did not take Art 151 in the fall. 2. He will attend Stanford or Yale. Hi did not attend Yale. Therefore, he attended Stanford. 3. If I had a nickel for every logic problem I have solved, then I would be rich. I have not received a nickel for every logic problem I have solved. Therefore, I am not rich. 4. If it is a dog, then it has fleas. It has fleas. Therefore, it is a dog. 5. If we serve salmon, then Vicky will join us for lunch. If Vicky will join us for lunch, then Marilyn will not join us for lunch. Therefore, if we serve salmon, Marilyn will not join us for lunch. 6. If I go to college, then I will not be able to work for my Dad. I did not go to college. Therefore, I went to work for my Dad.
Transcribed Image Text:LEARNING ACTIVITY 4.3 In exercises 1-6, determine whether the argument is valid or invalid by comparing its symbolic form into standard forms. For each valid argument, state the name of its standard form. 1. If you take Art 151 in the fall, you will be eligible to take Art 151 in the spring. You were not eligible to take Art 152 in the spring. Therefore, you did not take Art 151 in the fall. 2. He will attend Stanford or Yale. Hi did not attend Yale. Therefore, he attended Stanford. 3. If I had a nickel for every logic problem I have solved, then I would be rich. I have not received a nickel for every logic problem I have solved. Therefore, I am not rich. 4. If it is a dog, then it has fleas. It has fleas. Therefore, it is a dog. 5. If we serve salmon, then Vicky will join us for lunch. If Vicky will join us for lunch, then Marilyn will not join us for lunch. Therefore, if we serve salmon, Marilyn will not join us for lunch. 6. If I go to college, then I will not be able to work for my Dad. I did not go to college. Therefore, I went to work for my Dad.
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS