1 / 18

Understanding Validity in Arguments: Truth Tables and Logical Reasoning

This guide focuses on determining the validity of arguments using truth tables. It provides step-by-step instructions for evaluating premises and conclusions, ensuring clarity in logic problem-solving. By writing each premise on a separate line and using a horizontal line to separate the conclusion, students can construct truth tables effectively. The guide examines various argument forms, including Modus Ponens and Disjunctive Syllogism, and illustrates how to check for valid conclusions. This is an essential tool for students and enthusiasts of logic and mathematics.

cindy
Télécharger la présentation

Understanding Validity in Arguments: Truth Tables and Logical Reasoning

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. LogicChAPTER 3

  2. Truth TablesandValidity of Arguments3.6

  3. Problem Solving and Arguments Determining Validity 1. Write each premise on a separate line. 2. Write the conclusion after the premises and separate it by a horizontal line. 3. Make a truth table using a column for each premise and a column for the conclusion. 4. Check only the rows in which all the premises are true. For the argument to be valid, the conclusion must be also valid.

  4. Problem Solving and Arguments Symbolize each argument using the suggested abbreviations. In each case, determine the validity of the given argument.

  5. Problem Solving and Arguments Determine whether the argument is valid. If you study logic(s), mathematics is easy(e). Mathematics is not easy. . Therefore, you did not study logic.

  6. Problem Solving and Arguments 1 1 2 2 c c VALID

  7. Problem Solving and Arguments Determine whether the argument is valid. You will be eligible for a grant(e) if you meet all the criteria(m). You do not meet all the criteria. .∴So you are not eligible for a grant.

  8. Problem Solving and Arguments 1 1 2 2 c c INVALID

  9. Problem Solving and Arguments 1 1 2 Determine whether the argument is valid. c c VALID 2

  10. Problem Solving and Arguments Determine whether each argument is valid.

  11. SOLUTION: 1 2 c V A L I D

  12. SOLUTION: Equivalent

  13. Problem Solving and Arguments 1 1 2 2 c c VALID

  14. Problem Solving and Arguments 1 Find valid conclusions using all the premises. 3 4 c 2

  15. 1 4 2 valid 3 c

  16. Valid Argument Forms Modus Ponens Modus Tollens Hypothetical Disjunctive Syllogism Syllogism

  17. Problem Solving and Arguments If I drive to work, then I will not be late. If I am not late, then I do not lose any pay. Select the conclusion that will make each entire argument valid. a. If I am late, then I drive to work. b. If I do not lose any pay, then I drive to work. c. If I drive to work, then I do not lose any pay. d. If I do not drive to work, then I lose some pay.

  18. SOLUTION: If I drive to work, then I will not be late. p → q If I am not late, then I do not lose any pay. .q → r If I drive to work, then I will not lose any pay. p → r Hypothetical Syllogism a. If I am late, then I drive to work. ~q → p invalid b. If I do not lose any pay, then I drive to work. r → p invalid c. If I drive to work, then I will not lose any pay. p → r valid d. If I do not drive to work, then I lose some pay. ~p →~r invalid END

More Related