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(b) Explain why the truth table you In each of Exercises 10 through 15, determine whether the argument is valid by using truth tables. Specifically, check whether the conclusion is true for each case in which the conjunction of the premises is true. 10. 12. P-9 por P→~9 qvr Р :.r 11. pvq P 13. :~9 pv-q ~pvr :9-r

(b) Explain why the truth table you In each of Exercises 10 through 15, determine whether the argument is valid by using truth tables. Specifically, check whether the conclusion is true for each case in which the conjunction of the premises is true. 10. 12. P-9 por P→~9 qvr Р :.r 11. pvq P 13. :~9 pv-q ~pvr :9-r

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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(b) Explain why the truth table you completed shows that this argumen In each of Exercises 10 through 15, determine whether the argument is valid by using truth tables. Specifically, check whether the conclusion is true for each case in which the conjunction of the premises is true. 10. 12. 14. P-9 p➜r 9-r P→~9 qvr P ➖➖➖➖➖ 9~P qar :~p~r 19. You will fail this course if you do not study enough. You are not studying enough. Therefore, you will fail this course. 11. 22 If q. then not p. qand rare true. Therefore, if not p, then not r. 23. If a's are b's, then c's are d's. a's are not b's Therefore, e's are not d's. 13. LIDE pvq :~9 pv-q ~pvr :9-r 15. q➜r ~pvq SECTION 1.4: THINKING ABOUT VALID ARGUMENTS 20. If R, then not S. If not S, then 7. Therefore, if R, then T. 21. If a quadrilateral is a parallelogram, then its opposite sides are parallel. The opposite sides of quadrilateral ABCD are parallel. Therefore, ABCD is a parallelogram. Chapter 43
Transcribed Image Text:(b) Explain why the truth table you completed shows that this argumen In each of Exercises 10 through 15, determine whether the argument is valid by using truth tables. Specifically, check whether the conclusion is true for each case in which the conjunction of the premises is true. 10. 12. 14. P-9 p➜r 9-r P→~9 qvr P ➖➖➖➖➖ 9~P qar :~p~r 19. You will fail this course if you do not study enough. You are not studying enough. Therefore, you will fail this course. 11. 22 If q. then not p. qand rare true. Therefore, if not p, then not r. 23. If a's are b's, then c's are d's. a's are not b's Therefore, e's are not d's. 13. LIDE pvq :~9 pv-q ~pvr :9-r 15. q➜r ~pvq SECTION 1.4: THINKING ABOUT VALID ARGUMENTS 20. If R, then not S. If not S, then 7. Therefore, if R, then T. 21. If a quadrilateral is a parallelogram, then its opposite sides are parallel. The opposite sides of quadrilateral ABCD are parallel. Therefore, ABCD is a parallelogram. Chapter 43
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