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For Problems 30-39, use the TF method to test each argument for validity. Ifit is valid, construct a formal proof. If invalid, produce a counterexample chart. 30. p→r 31. w S ~wb b

For Problems 30-39, use the TF method to test each argument for validity. Ifit is valid, construct a formal proof. If invalid, produce a counterexample chart. 30. p→r 31. w S ~wb b

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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Need solution of question 30_ 37 odd and second pic need solution just question 41
In-Class Exercises and Problems for Section 3.1 149 For Problems 30–39, use the TFmethod to test each argument for validity. Ifit is valid, construct a formal proof. If invalid, produce a counterexample chart. 30. p→r 31. w→ s - w→ b 32. (p→q)→r 33. w→ (p^a) - (p^a) ~ W→ k k 35. a →(d v g) (dv g)→~ m 34. (pnq)→(rvs) ~ (rv s) ~ (p^q)→m a ~r- m 36. ~s(p<> q) 37. (cv d)→q s → (r v w) (rv w) → a a →r b→ a cvd 38. r→ w 39. (mv n) →w p→~ (r → w) ~ (a→ b) →~ (p^q) ~ (mv n) → (p ^q) (sv q) → b -p>(svq) b a →b
Transcribed Image Text:In-Class Exercises and Problems for Section 3.1 149 For Problems 30–39, use the TFmethod to test each argument for validity. Ifit is valid, construct a formal proof. If invalid, produce a counterexample chart. 30. p→r 31. w→ s - w→ b 32. (p→q)→r 33. w→ (p^a) - (p^a) ~ W→ k k 35. a →(d v g) (dv g)→~ m 34. (pnq)→(rvs) ~ (rv s) ~ (p^q)→m a ~r- m 36. ~s(p<> q) 37. (cv d)→q s → (r v w) (rv w) → a a →r b→ a cvd 38. r→ w 39. (mv n) →w p→~ (r → w) ~ (a→ b) →~ (p^q) ~ (mv n) → (p ^q) (sv q) → b -p>(svq) b a →b
is valid, construct a formal proof. If not, produce a counterexample chart. In Problems 40-43, express each argument symbolically. If the argument 40. If Georgia bans cigarette sales to eighteen-year- olds, then so will Alabama. Alabama will not ban cigarette sales to eighteen-year- eighteen-year-olds, then Louisiana will not. Louisiana plans to ban olds if Mississippi does not. If Mississippi bans cigarette sales to understand the signal. If an analog signal is sent to a computer, then it must be converted to a digital signal. If the computer cannot understand the analog signal, a modem is needed. Amodem is not needed. Therefore, the analog signal was not converted to a digital Modus Ponens, or MP, is the abbreviated form of modus ponendo ponens. In logic, this means "the mode that affirms by affirming." This is the valid form of an argument in which the antecedent (LHS) of a conditional statement is true, thereby concluding the truth Formal Proofs 150 a cigarette sales to eighteen-year-olds. Therefore, Georgia will no 41. If a diabetic patient has Type One diabetes, an insulin injection is used to lower blood sugar. If a diabetic patient has Type Two diabetes, an oral medication is taken to lower blood sugar. If the diabetic patient doesn't have Type Two diabetes, then the diabetic patient has Type One diabetes. The diabetic patient doesn't take oral medication to lower blood sugar. Therefore, the diabetic patient takes an insulin injection to lower blood sugar. join in the ban. 42. When interest rates are high, business costs increase. When business costs increase, consumer goods are more expensive. When consumer goods are more expensive, people do not purchase luxury items. People purchased luxury items. Therefore, interest rates were not high. 43. If an analog signal is sent to a computer, the computer camno. signal, DID YOU KNOW? of the consequent (RHS). Modus Tollens, or MT, is the abbreyint "the mode that denies by denu consequent (RHS) antecad
Transcribed Image Text:is valid, construct a formal proof. If not, produce a counterexample chart. In Problems 40-43, express each argument symbolically. If the argument 40. If Georgia bans cigarette sales to eighteen-year- olds, then so will Alabama. Alabama will not ban cigarette sales to eighteen-year- eighteen-year-olds, then Louisiana will not. Louisiana plans to ban olds if Mississippi does not. If Mississippi bans cigarette sales to understand the signal. If an analog signal is sent to a computer, then it must be converted to a digital signal. If the computer cannot understand the analog signal, a modem is needed. Amodem is not needed. Therefore, the analog signal was not converted to a digital Modus Ponens, or MP, is the abbreviated form of modus ponendo ponens. In logic, this means "the mode that affirms by affirming." This is the valid form of an argument in which the antecedent (LHS) of a conditional statement is true, thereby concluding the truth Formal Proofs 150 a cigarette sales to eighteen-year-olds. Therefore, Georgia will no 41. If a diabetic patient has Type One diabetes, an insulin injection is used to lower blood sugar. If a diabetic patient has Type Two diabetes, an oral medication is taken to lower blood sugar. If the diabetic patient doesn't have Type Two diabetes, then the diabetic patient has Type One diabetes. The diabetic patient doesn't take oral medication to lower blood sugar. Therefore, the diabetic patient takes an insulin injection to lower blood sugar. join in the ban. 42. When interest rates are high, business costs increase. When business costs increase, consumer goods are more expensive. When consumer goods are more expensive, people do not purchase luxury items. People purchased luxury items. Therefore, interest rates were not high. 43. If an analog signal is sent to a computer, the computer camno. signal, DID YOU KNOW? of the consequent (RHS). Modus Tollens, or MT, is the abbreyint "the mode that denies by denu consequent (RHS) antecad
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