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Logic ChAPTER 3

Logic ChAPTER 3. Truth Tables and Validity of Arguments 3.6. 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.

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Logic ChAPTER 3

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  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

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