Which of the following statements are logically equivalent ? A. Some fishes are not amphibians. B. Some fishes are amphibians. C. Some fishes are non-amphibians. D. Some non-amphibians are not non-fishes. Choose the correct answer from the options given below:
A, C and D only
To determine which statements are logically equivalent, let's analyze each option:
- Statement A: "Some fishes are not amphibians."
This means there exists at least one fish that does not belong to the category of amphibians. - Statement B: "Some fishes are amphibians."
This implies there exists at least one fish that is also an amphibian. - Statement C: "Some fishes are non-amphibians."
This can be rephrased as saying that there is at least one fish that does not belong to the category of amphibians, which is essentially the same as Statement A. - Statement D: "Some non-amphibians are not non-fishes."
By negating "non-fishes," we get "Some non-amphibians are fishes." This is logically equivalent to stating that there are some non-amphibians that are indeed fishes, which can be seen as similar to Statement A.
By analyzing the statements:
- Statement A and Statement C are logically equivalent because they both convey that not all fishes are amphibians; some are not.
- Statement D can be interpreted to support Statement A, as it implies the existence of fishes outside the amphibian category, aligning with Statement A's assertion.
- Statement B contradicts both A and C since it states that some fishes are amphibians, the opposite of what A and C assert.
Therefore, the logically equivalent statements are A, C, and D. This demonstrates a correct understanding of the logical relationships and equivalence between propositions.
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