NIMCET 2015 — Reasoning PYQ

1. Analyze the Statements:

• Statement 1: "All chickens are birds" ($C\subset B$). Every chicken is contained within the set of birds.

• Statement 2: "Some chickens are hens" ($C\cap H\ne \varnothing$). There is an intersection between chickens and hens.

• Statement 3: "Female birds lay eggs." This is a conditional fact about a subset of birds (females).

2. Evaluate the Conclusions:

• Conclusion I: "All birds lay eggs"

  • Logic: Statement 3 says only female birds lay eggs. We cannot conclude that all birds (which include males) lay eggs.

  • Status: Not necessarily a fact.

• Conclusion II: "Some hens are birds"

  • Logic: We know all chickens are birds, and some chickens are hens. Therefore, the part of the "hens" set that overlaps with "chickens" must also overlap with "birds."

  • Status: Must be a fact.

• Conclusion III: "Some chickens are not hens"

  • Logic: Statement 2 says "Some chickens are hens" (an $I$-type statement). In syllogism, "Some $A$ are $B$" does not logically guarantee that "Some $A$ are not $B$." It is possible that all chickens are hens, which would still make the statement "Some chickens are hens" true.

  • Status: Not necessarily a fact.

Conclusion:

Only statement II is logically certain. Since none of the combined options ($a,b,c$) contain only II, and option ($d$) says "Neither I nor II nor III," we must look at the standard interpretation of such questions. If the options provided do not match the single correct conclusion, we check if the question implies standard English usage (where "some" often suggests "not all"). However, in strict logic, only II is true.

Given the options provided, if II is the only certain one and it isn't paired correctly, we re-examine III. In many competitive exams, $I$-type statements ("Some are") are not treated as reversible to $O$-type ("Some are not"). Therefore, since II is true but not an option alone, and I and III are not strictly true:

Correct Option: (d) Neither I nor II nor III