Analyzing Arguments 1D

Determine the truth of the premises of the following argument. Then assess the strength of the argument and discuss the truth of the conclusion. ​ Premise: Chipmunks and dogs have four leg and are mammals ​Premise: Squirrels and mice have four legs and are mammals ​Premise: Lions and cows have four legs four legs and are mammals ​Conclusion: Iguanas have four legs​, so they are mammals

1 2 3 are true

Rephrase the​ argument, if​ necessary, so that the first premise is in the conditional form if​ p, then q. Identify the type of argument and determine its validity with a Venn diagram. If​ possible, discuss the truth of the premises and whether the argument is sound. ​Premise: If a corrosive is acid​, then it is dangerous Premise: HCL is a type of acid.HCL is a type of acid. Conclusion: HCL is dangerous. --- A. Denying the Conclusion B. Affirming the Conclusion C. Affirming the Hypothesis D. Denying the Hypothesis

C. Affirming the Hypothesis

Can a valid deductive argument be​ unsound? A. ​Yes, since the​ argument's conclusion could be true without it necessarily following from its premises. B. ​No, since a deductive argument must be sound for it to be valid. C. ​Yes, since the​ argument's conclusion could follow necessarily from its premises without the premises being true.

C. ​Yes, since the​ argument's conclusion could follow necessarily from its premises without the premises being true.

Decide whether the following statement makes sense​ (or is clearly​ true) or does not make sense​ (or is clearly​ false). Explain your reasoning. Through the logic of​ deduction, I will show you that if you accept the truth of my​ premises, you must also accept the truth of my conclusion. A. The statement makes sense. In a valid deductive​ argument, the conclusion must be true. B. The statement does not make sense. In a valid deductive​ argument, the conclusion must be true. C. The statement does not make sense. In a valid deductive​ argument, the conclusion follows necessarily from its premises. D. The statement makes sense. In a valid deductive​ argument, the conclusion follows necessarily from its premises.

D. The statement makes sense. In a valid deductive​ argument, the conclusion follows necessarily from its premises.

Premise: If a figure is a pentagon, then it has five sides premise: Hexagons have six sides Conclusion: Hexagons are not pentagons ----- What kind of argument is​ this? A. Denying the hypotheses B. Affirming the hypotheses C. Affirming the conclusion D. Denying the conclusion

D. Denying the conclusion

Fall months are windier than spring months. The wind must blow more often in November than in April.

Deductive The correct answer is DeductiveDeductive because the given argument makes a case for a specific conclusion from more general premises.

Which of the following are examples of inductive​ arguments? Select all that apply. A. ​Premise: ​(−​2)×​(3)=−6 ​Premise: ​(−​3)×​(1)=−3 ​Premise: ​(−​4)×​(2)=−8 ​Conclusion: The product of two negative numbers is negative. B. ​Premise: ​(-​2)×​(3)=−6 ​Premise: ​(−​3)×​(1)=−3 ​Premise: ​(−​4)×​(2)=−8 ​Conclusion: The product of a negative number and a positive number is negative. C. ​Premise: If a figure is a​ triangle, then it has three sides. ​Premise: Squares have four sides. ​Conclusion: Squares are not triangles. D. ​Premise: No country is an island. ​Premise: Iceland is an island. ​Conclusion: Iceland is not a country.

Premise: ​(−​2)×​(3)=−6 ​Premise: ​(−​3)×​(1)=−3 ​Premise: ​(−​4)×​(2)=−8 ​Conclusion: The product of a negative number and a positive number is negative.

Briefly explain the ideas of validity and soundness and how they apply to deductive arguments. Can a valid deductive argument be​ unsound? Can a sound deductive argument be​ invalid? Explain. Which of the following correctly explains the idea of​ validity? A. A deductive argument is valid if its conclusion follows necessarily from its premises. B. A deductive argument is valid if its conclusion follows necessarily from its premises and its conclusion is true. C. A deductive argument is valid if its conclusion follows necessarily from its premises and its premises are true. D. A deductive argument is valid if its conclusion follows necessarily from its premises and its premises and conclusion are all true. E. A deductive argument is valid if its conclusion might conceivably follow from its premises.

A) A deductive argument is valid if its conclusion follows necessarily from its premises.

Decide whether the following statement makes sense​ (or is clearly​ true) or does not make sense​ (or is clearly​ false). Explain your reasoning. Based on the testimonials of dozens of people who have lost weight following my​ diet, I will prove to you that my diet works for everyone. (This is an inductive argument) A. The statement does not make sense. Test cases never constitute a proof. B. The statement does not make sense. Some of the testamonials might not be in support of the diet. C. The statement makes sense. The diet would not have worked for so many people if it​ didn't work for everyone. D. The statement makes sense. Because the diet worked for that many​ people, it follows necessarily that the diet works for everyone.

A. The statement does not make sense. Test cases never constitute a proof.

Which of the following are properties of inductive​ arguments? Select all that apply.

1. A conclusion is formed by generalizing from a set of more specific premises. 2. It can be analyzed only in terms of its strength. 3. It cannot prove its conclusion true. At​ best, it shows that its conclusion probably is true.

Identify the argument as inductive or deductive. Every coach must know his sport well. Marty Wright is a baseball​ coach, so Marty Wright knows baseball well.

Deductive

Can inductive logic be used to prove a mathematical​ theorem? Explain. A. ​Yes, since all mathematical proofs are inductive arguments. B. ​Yes, since sufficiently many test cases can constitute a proof. C. ​No, since test cases are never enough to satisfy yourself of a​ rule's truth. D. ​No, since test cases never constitute a proof.

D. ​No, since test cases never constitute a proof.

Which of the following are examples of deductive​ arguments? Select all that apply. A. ​Premise: No country is an island. ​Premise: Iceland is an island. ​Conclusion: Iceland is not a country. Your answer is correct. B. ​Premise: ​(minus−​2) times ×​(3)equals=minus−6 ​Premise: ​(minus−​3) times ×​(1)equals=minus−3 ​Premise: ​(minus−​4) times ×​(2)equals=minus−8 ​Conclusion: The product of a negative number and a positive number is negative. C. ​Premise: If a figure is a​ triangle, then it has three sides. ​Premise: Squares have four sides. ​Conclusion: Squares are not triangles. Your answer is correct. D. ​Premise: ​(minus−​2) times ×​(3)equals=minus−6 ​Premise: ​(minus−​3) times ×​(1)equals=minus−3 ​Premise: ​(minus−​4) times ×​(2)equals=minus−8 ​Conclusion: The product of two negative numbers is negative.

A and C

Can a sound deductive argument be​ invalid? A. ​No, since a deductive argument must be valid for it to be sound. B. ​Yes, since the​ argument's conclusion could follow necessarily from its premises without the premises being true. C. ​Yes, since the​ argument's conclusion could be true without it necessarily following from its premises.

A. ​No, since a deductive argument must be valid for it to be sound.

Which of the following correctly explains the idea of​ soundness? A. A deductive argument is sound if its conclusion might conceivably follow from its premises. B. A deductive argument is sound if its conclusion follows necessarily from its premises and its premises are true. C. A deductive argument is sound if its conclusion follows necessarily from its premises. D. A deductive argument is sound if its conclusion follows necessarily from its premises and its premises and conclusion are all true. E. A deductive argument is sound if its conclusion follows necessarily from its premises and its conclusion is true.

B. A deductive argument is sound if its conclusion follows necessarily from its premises and its premises are true.

Consider the following proposition. If Company A takes market share from Company B by manufacturing hybrid cars while Company B is still making​ SUVs, Company B is punished by the market. ​(a) What is the logical conclusion​ (if any) in the event that company A takes market share from Company B by manufacturing hybrid cars while Company B is still making​ SUVs? ​(b) What is the logical conclusion​ (if any) in the event that Company B is not punished by the​ market? ​(c) Can you draw any conclusion about what happens if Company A makes SUVs and Company B makes hybrid​ cars? ---------------- A. Company B is not punished by the market. B. Company B starts making hybrid cars. C. Company B is punished by the market. D. There is no logical conclusion.

C. Company B is punished by the market.