Download presentation

Presentation is loading. Please wait.

Published bySteve Harler Modified over 4 years ago

1
Logic ChAPTER 3 1

2
Truth Tables and Validity of Arguments 3.6 2

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. 3

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

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

6
Problem Solving and Arguments 6 ses → e~ e~ s TTTFF TFFTF FTTFT FFTTT VALID 1 2 c 1 2 c

7
Problem Solving and Arguments 7 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. Determine whether the argument is valid.

8
Problem Solving and Arguments 8 mem → e~ m~ e TTTFF TFFFT FTTTF FFTTT INVALID 1 2c 1 2 c

9
Problem Solving and Arguments 9 pqp → qpq TT TF FT FF VALID Determine whether the argument is valid. T F T T T T F F T F T F 2 1 c 1 2 c

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

11
11 SOLUTION: pqrp → qq → r ~ r~ p ~ r → ~ p TTT TTF TFT TFF FTT FTF FFT FFF T T F F T T T T T F T T T F T T V A L I D F T F T F T F T F F F F T T T T T F T F T T T T c 1 2

12
SOLUTION: pr~r~r~ p~ p~ r → ~ p~ r → ~ p T T F F T F T F F T F T F F T T T F T T prp → r T T F F T F T F T F T T Equivalent 12

13
pqrp → qq → rp → r TTT TTF TFT TFF FTT FTF FFT FFF T F T F T T T T Problem Solving and Arguments 13 VALID T T F F T T T T T F T T T F T T 12c 1 2 c

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

15
pqrsp → qq → r~ s~ r~ s → ~ rp TTTT TTTF TTFT TTFF TFTT TFTF TFFT TFFF FTTT FTTF FTFT FTFF FFTT FFTF FFFT FFFF T T T T F F F F T T T T T T T T T T F F T T T T T T F F T T T T F T F T F T F T F T F T F T F T F F T T F F T T F F T T F F T T T F T T T F T T T F T T T F T T T T T T T T T T F F F F F F F F s T F T F T F T F T F T F T F T F valid 15 123 c 4

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

17
Problem Solving and Arguments 17 Select the conclusion that will make each entire argument valid. If I drive to work, then I will not be late. If I am not late, then I do not lose any pay. 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: c. If I drive to work, then I will not lose any pay. p → r valid 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 a. If I am late, then I drive to work. ~q ~q → p invalid Hypothetical Syllogism b. If I do not lose any pay, then I drive to work. r → p invalid If I drive to work, then I will not lose any pay. p → r d. If I do not drive to work, then I lose some pay. ~p ~p →~r invalid 18 END

Similar presentations

© 2019 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google