Determine if valid or invalid. Using of Rules of Inference.30. If you are kind to a puppy, then he will be your friend. You weren’t kind to that puppy. Hence, he isn’t your friend. SymbolsNamesRuleGiven a statement, it is permissible to infer anydisjunction having that statement as one disjunct.1.Addition..P VQRules ofPAQ PAQ2.Qor PSimplificationSimplification either of its conjuncts separately.Inference..P..QGiven two statements, it is permissible to infer theconjunction having them as conjuncts.3.QConjunction..PAQP- QGiven a conditional, and given the antecedent of4. PModus Ponensthat same conditional, it is permissible to infer theconsequent of the same conditional.P.Given a conditional, and given the NEGATION of itsCONSEQUENT, it is permissible to infer theNEGATION of its antecedent.Given two conditionals such that the consequentof one matches the antecedent of the other, it ispermissible to infer a conditional having theUNMATCHED antecedent and the UNMATCHED5.Modus TollensP - QHypotheticalSyllogism(Transitivity)Q-R6. .. P-Rconsequent.P VQPVQDisjunctiveSylogism(Cancellation) disjuncts.Given a disjunction, and given the denial of oneof its disjuncts, it is permissible to infer the other7. -Por -Q..Q.PP - QGiven two conditionals (or a conjunction of twoconditionals) and given the disjunction of theirantecedents, it is permissible to infer thedisjunction of their consequents.8. PVRConstructiveDilemma.QVSP - QR -S9.-QV-SDestructiveDilemma..-P V -RP+QP+QGiven a biconditional, and given one side of thatsame, biconditional, it is permissible to infer theother side of that biconditional.10. РorQEquivalence.QPGiven a statement, it is permissible to infer that theRepetition11. ..PP → Q12. ..Р—(РЛQ)same statement.Absorption

Solution: Let us define the following symbols: k = kind to puppy f = puppy…

Answered: If you are kind to a puppy, then he…

Math

Advanced Math

If you are kind to a puppy, then he will be your friend. You weren’t kind to that puppy. Hence, he isn’t your friend.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: A politician is interested in the proportion of voters in his district that think he is doing a good…

A: Given : The above option is representing a randomly selected sample out of the population…

Q: 17. What possible misuse or misinterpretation may exist in the following statement? The Stay Healthy…

A: Given that The Stay Healthy Candy Bar indicates on its label that it has no cholesterol. Therefore…

Q: Determine the regression equation 1 2 3 4 5 6. 7 8 y 0,5 0,8 1,2 1,9 3 4,8 7,5 11,9

A: Note: Commas are taken as decimals for computation. Mean x=∑xin=(1+2+3+4+5+6+7+8)/8=36/8=4.5Mean…

Q: We survey 200 students, and ask each whether they like donuts, pizza, and/or tacos. Every student…

Q: Let the students who likes table tennis be 12, the ones who like lawn tennis 10, those who like only…

Q: This makes sense because the Chevalier used the same logic to win great sums of money. B. This…

A: Given statement, My chance of getting a 5 on the roll of one die is 1/6,so my chance of getting at…

Q: 2.) A group of students in a mathematics class were asked whether they participated in the past 3…

A: Given the survey results of participation in the past 3 presidential elections (2020, 2016, and…

Q: 21. An online survey is used to monitor customer service. The survey consists of 14 questions. Ten…

Q: __________

Q: Car insurance covers damage caused by accidents or other mishaps. Which of the following situations…

A: The objective of this question is to identify which of the given situations would be covered by…

Q: Rude Drivers: Tailgating Do you tailgate the car in front of you? About 35% of all drivers will…

Q: () Percentage of viewers who are 18 to 34 and prefer videos on a mobile or laptop device. Percentage…

A: From the provided information, Viewer age Mobile/Laptop Device TV Screen Row Total 18…

Q: 53. Rudy surveyed 80 people about whether they prefer blueberry or cherry pie and whether they…

Q: Jane surveys a random sample of 200 students from her middle school to learn what type of school…

A: Obtain the sample proportion of students who prefer sandwich: It is given that among a sample of 200…

Q: 2.) A group of students in a mathematics class were asked whether they participated in the par…

A: 2.) A group of students in a mathematics class were asked whether they participated in the past 3…

Q: Use the following results from a test for marijuana use, which is provided by a certain drug testing…

A: Introduction: A false positive result in this case is a result in which the test result is positive,…

Q: 2. A class wants to know who in their town likes basketball. The class asks people at the mall.…

A: Convenience sampling is a nonprobability sampling that does not depend on chance. Instead of…

Q: Two persons participated in five shooting competition and were able to hit the target correctly out…

A: Given: n=5 The data is given as: Competitor A Competitor B 6 12 12 15 12 7 10 7 7…

Q: This Q One fact in a fact family is 2+5= 7. Complete parts (a) and (b) below. ..... a. What are the…

Q: U is the set of furniture stores. A is the set of furniture stores that sell couches. B is the set…

A: Given: U is the set of furniture stores.A is the set of furniture stores that sell couches.B is the…

Q: ix faculty members (F) are on a panel discussing a ways can the nine participants be lined up at a…

Q: The graph below shows the ages in months of the boys and girls in Mrs. Duncan's nursery class. Mrs.…

A: We have to select correct conclusion from the following statements using the data given in the bar…

Q: 11. Three people (X, Y, Z) are in a room with you. One is a knight (knights always tell the truth),…

Q: Write a function for the blue graph of a quadratic function in a form: f(x) = a ( b (x + c))² + d…

A: The given parent graph is shown by red and transformed graph shown by blue in the question.

Question

Determine if valid or invalid. Using of Rules of Inference.

30. If you are kind to a puppy, then he will be your friend. You weren’t kind to that puppy. Hence, he isn’t your friend.

Symbols
Names
Rule
Given a statement, it is permissible to infer any
disjunction having that statement as one disjunct.
1.
Addition
..P VQ
Rules of
PAQ PAQ
2.
Q
or P
Simplification
Simplification either of its conjuncts separately.
Inference
..P
..Q
Given two statements, it is permissible to infer the
conjunction having them as conjuncts.
3.
Q
Conjunction
..PAQ
P- Q
Given a conditional, and given the antecedent of
4. P
Modus Ponens
that same conditional, it is permissible to infer the
consequent of the same conditional.
P.
Given a conditional, and given the NEGATION of its
CONSEQUENT, it is permissible to infer the
NEGATION of its antecedent.
Given two conditionals such that the consequent
of one matches the antecedent of the other, it is
permissible to infer a conditional having the
UNMATCHED antecedent and the UNMATCHED
5.
Modus Tollens
P - Q
Hypothetical
Syllogism
(Transitivity)
Q-R
6. .. P-R
consequent.
P VQ
PVQ
Disjunctive
Sylogism
(Cancellation) disjuncts.
Given a disjunction, and given the denial of one
of its disjuncts, it is permissible to infer the other
7. -P
or -Q
..Q
.P
P - Q
Given two conditionals (or a conjunction of two
conditionals) and given the disjunction of their
antecedents, it is permissible to infer the
disjunction of their consequents.
8. PVR
Constructive
Dilemma
.QVS
P - Q
R -S
9.
-QV-S
Destructive
Dilemma
..-P V -R
P+Q
P+Q
Given a biconditional, and given one side of that
same, biconditional, it is permissible to infer the
other side of that biconditional.
10. Р
or
Q
Equivalence
.Q
P
Given a statement, it is permissible to infer that the
Repetition
11. ..P
P → Q
12. ..Р—(РЛQ)
same statement.
Absorption

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

1.2 EXERCISES Which of the following are statements? Why or why not? a. George Washington was the first president of the United States. 4. b. Abraham Lincoln was the second president of the United States. c Who was the first vice president of the United States? d. Abraham Lincoln was the best president. Which of the following are statements? Why or why
Ms. Kradin surveyed the $84$84 students that she teaches and asked them if they preferred to play soccer or basketball. The results are displayed in the table below. Soccer Basketball Total 11th graders $28$28 $20$20 $48$48 12th graders $21$21 $15$15 $36$36 Total $49$49 $35$35 $84$84 Which of the following statements are true? Select all that apply. Responses A 11th graders and 12th graders are equally likely to prefer soccer. 11th graders and 12th graders are equally likely to prefer soccer. B A 12th grade student is less likely to prefer soccer than an 11th grade student. A 12th grade student is less likely to prefer soccer than an 11th grade student. C An 11th grade student is more likely to prefer basketball than a 12th grade student. An 11th grade student is more likely to prefer basketball than a 12th grade student. D The data does not suggest there is an association between what grade the students are in and their preference of…
blems iaundera Grady: Attempt 2 # Your Answer: $ Answer asked what they did last Friday night. It found: • 165 watched TV 173 hung out with friends . 35 watched TV and ate pizza, but did not hang out with friends • 44 watched TV and hung out with friends, but did not eat pizza • 42 hung out with friends and ate pizza, but did not watch TV • 36 watched TV, hung out with friends, and ate pizza • 94 did not do any of these three activities How may 18-24 year olds (of these three activities) only ate pizza last Friday night? Su 21 Knowledge Base % f6 €3 e f7 Contacts (Allianz) & hp fg CC CO 8 19 [) ( General and POS (S... 9 f10 NT с fil Custo CE 85 f12 num lk
An association studies the ethnicity of moviegoers to understand changes in the demographics of moviegoers over time. The accompanying table displays the numbers of moviegoers (in millions) classified as to whether they were Hispanic, African-American, Caucasian, and Other for a certain year. Also included are the numbers for the general population and the number of tickets sold. Complete parts a and b below. E Click the icon to view the table of results. a) Construct the conditional proportions of Ethnicity for all three groups: the entire population, moviegoers, and ticket holders. TITI Caucasian Hispanic African-American Other Population % Moviegoers % % Tickets % % % % (Round to one decimal place as needed.) b) Write a brief description of the association between population groups and Ethnicity. The distribution of moviegoers is V the population as a whole. seem to buy proportionally more tickets than the other ethnic groups and appear to buy proportionally fewer tickets. V appear…
Only looking for a, b, and c.
Robin is listening for the phone to ring. Which of these depicts a correct decision (1-?)? a.Robin checks their phone when it rings. b.Robin does not check their phone when it doesn't ring. c.Robin checks their phone when it does not ring. d.Robin does not check their phone when it rings.
150 students were polled. 75 of them are learning Hindi. 60 of them are learning Italian. 40 of them are learning neither Hindi nor Italian. How many of them are learning both Hindi and Italian? 4
17. What possible misuse or misinterpretation may exist in the following statement? The Stay Healthy Candy Bar indicates on its label that it has no cholesterol. Therefore it is safe to eat as many of these candy bars as you want.
Let R = {(a, b), (b, a),(a, c), (c, d), (d, a)} a. Is (a, c) E R³? b. Is (a, a) E R²? c. Is (c, c) E R5? d. For what values of k < 5 is (a, d) € Rk?
A coach of a cross country team asked all 200 of the runners who ran at a meet two questions: Did you get less than 8 hours of sleep last night? Yes No Did you achieve a personal record in this meet? Yes No The coach saw an association between the amount of sleep and achieving a personal record for the runners. Which statement provides evidence for this association?
2. A class wants to know who in their town likes basketball. The class asks people at the mall. Which of the following is the best description of the convenience example? A. The sample is not representative because the group surveyed is probably not biased about basketball. B. The sample is not representative because the group surveyed is probably biased about basketball. C. The sample is representative because the group surveyed is probably biased about basketball. D. The sample is representative because the group surveyed is probably not biased about basketball. If a convenience sample is considered to be not representative, how could it be representative, how could it be made into a representative sample?
39. An environmental scientist wants to test the null hypothesis that an antipollution device for cars is not effective. Under which of the following conditions would a Type I error be committed? The scientist concludes that the antipollution device is effective when actually it is. The scientist concludes that the antipollution device is not effective when actually it is not. The scientist concludes that the antipollution device is not effective when actually it is. The scientist concludes that the antipollution device is effective when actually it is not.