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Given Argument Q=B N. (O v P) (N•P) > ~(Q v B) Conclusion: (~Qv~B) • ~(NO) Premise 1: Premise 2: Premise 3:

Given Argument Q=B N. (O v P) (N•P) > ~(Q v B) Conclusion: (~Qv~B) • ~(NO) Premise 1: Premise 2: Premise 3:

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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6. Multiline Indirect Truth Tables for Validity - Practice 1 If there is more than one way to make the premises of an argument true and the conclusion of the argument false, an indirect truth table for the argument will require more than one line. In this case, either select one of the premises and compute all of the ways it can be made true, or select the conclusion and compute all of the ways it can be made false. Having made your selection, compute the truth values in each line, beginning with the first line. Whenever you complete any line without deriving a contradiction, stop! The argument has been proved invalid. If you derive a contradiction on the first line, proceed to the second line. If no contradiction is derived on the second line, again, stop because the argument has been proved invalid. If you derive a contradiction on the second line, proceed to the third line, and so on. If each of the lines necessarily leads to a contradiction, the argument is valid. Solve the indirect truth table for this argument: Given Argument Q = B N• (O v P) (N•P) > ~(Q v B) (~Qv~B) • ~(N• O) Premise 1: Premise 2: Premise 3: Conclusion: On paper, construct an indirect truth table for the given argument. (Note: a correct indirect truth table for this argument will require more than one line.) Then explain your results by filling in the following statements. True or False Assumptions: The premises were assumed to be Results: Since this assumption results in True or False and the conclusion to be a contradiction on every line or at least one line without a contradiction valid or the argument is invalid
Transcribed Image Text:6. Multiline Indirect Truth Tables for Validity - Practice 1 If there is more than one way to make the premises of an argument true and the conclusion of the argument false, an indirect truth table for the argument will require more than one line. In this case, either select one of the premises and compute all of the ways it can be made true, or select the conclusion and compute all of the ways it can be made false. Having made your selection, compute the truth values in each line, beginning with the first line. Whenever you complete any line without deriving a contradiction, stop! The argument has been proved invalid. If you derive a contradiction on the first line, proceed to the second line. If no contradiction is derived on the second line, again, stop because the argument has been proved invalid. If you derive a contradiction on the second line, proceed to the third line, and so on. If each of the lines necessarily leads to a contradiction, the argument is valid. Solve the indirect truth table for this argument: Given Argument Q = B N• (O v P) (N•P) > ~(Q v B) (~Qv~B) • ~(N• O) Premise 1: Premise 2: Premise 3: Conclusion: On paper, construct an indirect truth table for the given argument. (Note: a correct indirect truth table for this argument will require more than one line.) Then explain your results by filling in the following statements. True or False Assumptions: The premises were assumed to be Results: Since this assumption results in True or False and the conclusion to be a contradiction on every line or at least one line without a contradiction valid or the argument is invalid
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