Observe the following argument and pick the correct answer: All pigs are…
2023
Observe the following argument and pick the correct answer:
All pigs are sheep.
All sheep are goats.
Therefore, all pigs are goats.
A. A valid argument because if the premises were true the conclusion would have been true.
B. An invalid argument because the conclusion does not follow from the premises.
C. The conclusion is probably true.
D. It is a weak argument.
Choose the correct answer from the options given below:
Answer: A. A only — ConceptA deductive argument is valid when the conclusion must be true whenever all its premises are true. Universal class inclusion is transitive: if every…
- A.
A only
- B.
B and D only
- C.
C and D only
- D.
D only
Show answer & explanation
Correct answer: A
Concept
A deductive argument is valid when the conclusion must be true whenever all its premises are true.
Universal class inclusion is transitive: if every member of class P belongs to S and every member of S belongs to G, then every member of P belongs to G.
Application
Represent the premises as P ⊆ S and S ⊆ G, where P, S, and G denote pigs, sheep, and goats.
By transitivity of inclusion, P ⊆ G; therefore, every pig is a goat whenever the premises are true.
The conclusion follows necessarily rather than merely probably, so the argument is deductively valid.
Cross-check and contrast
The statement that calls the argument valid uses the correct truth-preservation test.
The statement that calls it invalid ignores the transitive inclusion chain.
The statement that says the conclusion is probably true weakens a necessary consequence into a probabilistic claim.
The statement that calls the argument weak applies inductive-strength language to a deductive argument.
Thus the premises truth-preserve the stated conclusion, while the probabilistic and strength-based classifications do not apply.