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validity. If the argument is invalid, produce a counterexample chart 1. (-m→p)→r In-Class Exercises 2. a → b m a ~mvb 4. - pv (~a→b) 3. rv(~p→s) -r>(-sv p) ~ avc pvr 6. (cv d)>g a → (bv c) 5. (pvq)r a -dg 7. WA(avb) -av (c-→s) w->(~svn) 8. w→s (svr)→9 c(nvb) pv (w→r)

validity. If the argument is invalid, produce a counterexample chart 1. (-m→p)→r In-Class Exercises 2. a → b m a ~mvb 4. - pv (~a→b) 3. rv(~p→s) -r>(-sv p) ~ avc pvr 6. (cv d)>g a → (bv c) 5. (pvq)r a -dg 7. WA(avb) -av (c-→s) w->(~svn) 8. w→s (svr)→9 c(nvb) pv (w→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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Solve 5,6,7 indirect method and just 13
not know the truth value of an indirect approach. Therefore, we will counterexample chart using the truth values obtained, we write: a b |c So. Hence, our argument is invalid. Constructing a In-Class Exercises and Problems for Section 2.5 In-Class Exercises validity. If the argument is invalid, produce a counterexample chart 1. (~m→p)→r 2. a → b m → a -rvq - m v b 3. rv(~p→s) 4. -pv(~a→b) -r(-sv p) pvr ~ avc 5. (pvq)-r 6. (cv d)>g a→ (bvc) a -d→g 7. wA(avb) -av(c→s) 8. w→S w(~svn) (svr)→q c> (nvb) pv (w→r)
Transcribed Image Text:not know the truth value of an indirect approach. Therefore, we will counterexample chart using the truth values obtained, we write: a b |c So. Hence, our argument is invalid. Constructing a In-Class Exercises and Problems for Section 2.5 In-Class Exercises validity. If the argument is invalid, produce a counterexample chart 1. (~m→p)→r 2. a → b m → a -rvq - m v b 3. rv(~p→s) 4. -pv(~a→b) -r(-sv p) pvr ~ avc 5. (pvq)-r 6. (cv d)>g a→ (bvc) a -d→g 7. wA(avb) -av(c→s) 8. w→S w(~svn) (svr)→q c> (nvb) pv (w→r)
of 9. pb 10. - pVs r>(-pvs) s (m→r) c(rv w) тль w (s→r) cr For Exercises 11-12, each set of premises is followed by four possible conclusions. State the conclusion(s) that makes the argument valid. There may be more than one correct conclusion. Be sure to state all that apply. 11. Ь 12. ~ w a+ (mv~n) (nv p)→-r (mv p)→-b (bAc) w - CV~ m (a→r)vw a. w a. r b. c b. p n C. wV ~C C. - m d. - w d. - P In Exercises 13-14, express each argument symbolically. Then determine if it is valid or invalid. If it is invalid, produce a counterexample chart. 13. If I pass my required math class with at least a C, the credits will transfer. If the credits don't transfer or I change my major, I will be behind in my course load. Either I am not behind in my course load or I pass my required math class with at least a C. Therefore, if I don't change my major, the credits will transfer. 14. Jill can't afford to go to college. Here are the scholarship offers she knows she can count on. If college A gives a scholarship then college B will also give a scholarship but college C won't. If college C gives a scholarship, then college A will too. College B decided to give a scholarship. Can Jill determine that either college A or college C will also offer a scholarship?
Transcribed Image Text:of 9. pb 10. - pVs r>(-pvs) s (m→r) c(rv w) тль w (s→r) cr For Exercises 11-12, each set of premises is followed by four possible conclusions. State the conclusion(s) that makes the argument valid. There may be more than one correct conclusion. Be sure to state all that apply. 11. Ь 12. ~ w a+ (mv~n) (nv p)→-r (mv p)→-b (bAc) w - CV~ m (a→r)vw a. w a. r b. c b. p n C. wV ~C C. - m d. - w d. - P In Exercises 13-14, express each argument symbolically. Then determine if it is valid or invalid. If it is invalid, produce a counterexample chart. 13. If I pass my required math class with at least a C, the credits will transfer. If the credits don't transfer or I change my major, I will be behind in my course load. Either I am not behind in my course load or I pass my required math class with at least a C. Therefore, if I don't change my major, the credits will transfer. 14. Jill can't afford to go to college. Here are the scholarship offers she knows she can count on. If college A gives a scholarship then college B will also give a scholarship but college C won't. If college C gives a scholarship, then college A will too. College B decided to give a scholarship. Can Jill determine that either college A or college C will also offer a scholarship?
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