Which of the following statements are logically equivalent. A. No monkeys are…
2024
Which of the following statements are logically equivalent.
A. No monkeys are felines.
B. Some monkeys are felines.
C. Some felines are monkeys.
D. Some monkeys are not feline.
Choose the correct answer from the options given below:
Answer: B. B and C only — Concept — Two categorical statements are logically equivalent only when each one entails the other, so that they are true in exactly the same situations. In…
- A.
A and D only
- B.
B and C only
- C.
B and D only
- D.
B, C and D only
Show answer & explanation
Correct answer: B
Concept — Two categorical statements are logically equivalent only when each one entails the other, so that they are true in exactly the same situations. In traditional logic the operation that exchanges the subject term and the predicate term of a statement is called conversion. Simple conversion preserves truth in both directions only for E-type statements ("No S are P") and I-type statements ("Some S are P"); it is invalid for A-type ("All S are P") and O-type ("Some S are not P") statements.
Application — Classify each of the four statements by its quantity (universal or particular) and its quality (affirmative or negative), and note which term sits in the subject position.
Statement | Quantity and quality | Type | Subject to predicate |
|---|---|---|---|
A. No monkeys are felines. | Universal negative | E | monkeys to felines |
B. Some monkeys are felines. | Particular affirmative | I | monkeys to felines |
C. Some felines are monkeys. | Particular affirmative | I | felines to monkeys |
D. Some monkeys are not felines. | Particular negative | O | monkeys to felines |
B and C are the same I-type statement with the two terms exchanged, so each is the converse of the other. Simple conversion of an I-type statement is valid in both directions: if at least one monkey is also a feline, then that very individual is a feline that is also a monkey, and reading the overlap from the other side gives the second statement. Symbolically both say the same thing, that the class of monkeys and the class of felines share at least one member. B and C therefore assert exactly one and the same fact and are logically equivalent.
Cross-check — Test every other grouping the same way, in both directions:
A against B or C: A denies that monkeys and felines share any member, while B and C assert that they share at least one. A is the contradictory of each, so the two cannot even be true together, let alone be equivalent.
D against B or C: "Some monkeys are not felines" stays true whether or not some other monkey happens to be a feline, so it neither entails B or C nor follows from them.
A against D: under the traditional assumption that monkeys exist, A entails D by subalternation, but D never entails A, since D leaves room for a further monkey that is a feline. One-way entailment is weaker than equivalence.
Converting an O-type statement is invalid: "Some felines are not monkeys" does not follow from "Some monkeys are not felines", which is why D finds no equivalent partner among the four statements.
Result — Only B and C are logically equivalent, so the correct choice is "B and C only".