Question

The question contains six statements followed by four sets of combination of three. Choose the set in which the statements are logically related.

Statements:
(i) All frogs are amphibians.
(ii) All amphibians are not frogs.
(iii) All amphibians are cold blooded.
(iv) All frogs lay eggs.
(v) All amphibians lay eggs.
(vi) Frogs are cold blooded.

• A. i, iii, vi
• B. i, iv, v
• C. i, ii, v
• D. ii, v, iv

Hint:

Two of the statements should nest one class inside another and then inside a third. Track which class appears in both premises and then disappears.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
We want the set of three statements where two are premises and the third follows from them. Judge only by the logic of the statements given, not by outside knowledge of biology.

Step 2: Key Formula or Approach:
Apply the chain rule for universal statements. If All A are B and All B are C, then All A are C. The middle term B must be present in both premises and absent from the conclusion.

Step 3: Detailed Explanation:
Check option (A), which is i, iii, vi.
Premise (i): All frogs are amphibians, placing frogs inside the class of amphibians.
Premise (iii): All amphibians are cold blooded, placing amphibians inside the class of cold blooded creatures.
The middle term is amphibians. Frogs lie inside amphibians, amphibians lie inside cold blooded creatures, so frogs lie inside cold blooded creatures.
Conclusion (vi): Frogs are cold blooded. Valid, and amphibians has correctly dropped out of the conclusion.

Step 4: Testing the other options:
Option (B) is i, iv, v. From all frogs are amphibians and all frogs lay eggs, the most you can get is that some amphibians lay eggs, because frogs are only a part of the amphibian class. Concluding (v), all amphibians lay eggs, extends a property from a subset to the whole class, which is not allowed.
Option (C) is i, ii, v. Statement (ii) is a negative remark and (v) is about all amphibians laying eggs, but egg laying never appears in (i) or (ii), so it cannot come out of them.
Option (D) is ii, v, iv. Here (v) says all amphibians lay eggs, and getting to (iv), all frogs lay eggs, would need the premise that frogs are amphibians, which is (i). Statement (ii) does not supply that link, so the set is incomplete.

Step 5: Final Answer:
The valid chain is i, iii, vi, so the answer is option (A).