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Determine if the following is a valid deduction rule: P→ Q -Q TF First, make a truth table for the relevant statements. (You might want to complete the truth table on paper so you can make columns for intermediate steps; just record the final columns here.) PQ P→ Q T|T FT F F A - -> .. -> -P -Q A - -> -> -P Is the deduction rule valid? O A. Yes, in every row where both premises are true, the conclusion is also true. ○ B. No, because the columns for the two premises are not identical. C. No, because the conclusion is not always true. D. Yes, because there is a row in which both premises are true. O E. Impossible to determine without more information.

Determine if the following is a valid deduction rule: P→ Q -Q TF First, make a truth table for the relevant statements. (You might want to complete the truth table on paper so you can make columns for intermediate steps; just record the final columns here.) PQ P→ Q T|T FT F F A - -> .. -> -P -Q A - -> -> -P Is the deduction rule valid? O A. Yes, in every row where both premises are true, the conclusion is also true. ○ B. No, because the columns for the two premises are not identical. C. No, because the conclusion is not always true. D. Yes, because there is a row in which both premises are true. O E. Impossible to determine without more information.

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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Determine if the following is a valid deduction rule: P→ Q -Q TF First, make a truth table for the relevant statements. (You might want to complete the truth table on paper so you can make columns for intermediate steps; just record the final columns here.) PQ P→ Q T|T FT F F A - -> .. -> -P -Q A - -> -> -P Is the deduction rule valid? O A. Yes, in every row where both premises are true, the conclusion is also true. ○ B. No, because the columns for the two premises are not identical. C. No, because the conclusion is not always true. D. Yes, because there is a row in which both premises are true. O E. Impossible to determine without more information.
Transcribed Image Text:Determine if the following is a valid deduction rule: P→ Q -Q TF First, make a truth table for the relevant statements. (You might want to complete the truth table on paper so you can make columns for intermediate steps; just record the final columns here.) PQ P→ Q T|T FT F F A - -> .. -> -P -Q A - -> -> -P Is the deduction rule valid? O A. Yes, in every row where both premises are true, the conclusion is also true. ○ B. No, because the columns for the two premises are not identical. C. No, because the conclusion is not always true. D. Yes, because there is a row in which both premises are true. O E. Impossible to determine without more information.
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