NIMCET 2010 — Reasoning PYQ

Analysis of Options:

• (a) All elephants are wild. All lions are wild. So all lions are elephants.

  • $\text{Elephant}\subset \text{Wild}$ and $\text{Lion}\subset \text{Wild}$.

  • This does not mean $\text{Lion}\subset \text{Elephant}$. The conclusion is Invalid.

• (b) All mangoes are red. Some apples are mangoes. So all apples are red.

  • $\text{Mango}\subset \text{Red}$. Some $\text{Apples}$ are $\text{Mangoes}$.

  • This only implies "Some apples are red," not "all." The conclusion is Invalid.

• (c) All roads are boxes. All foxes are roads. So all boxes are foxes.

  • $\text{Road}\subset \text{Box}$ and $\text{Fox}\subset \text{Road}$.

  • This means $\text{Fox}\subset \text{Box}$ (All foxes are boxes). It does not mean all boxes are foxes. The conclusion is Invalid.

• (d) All $XYZ$ can run. All $ABC$ are $XYZ$. So all $ABC$ can run.

  • Let $R$ be the set of things that can run.

  • Premise 1: $XYZ\subset R$

  • Premise 2: $ABC\subset XYZ$

  • By transitive property:

    $$ABC\subset XYZ\text{ and }XYZ\subset R⟹ABC\subset R$$

  • Therefore, "All $ABC$ can run" is Logically Valid.

Conclusion:

In option (d), the third statement is a direct logical consequence of the first two.

Correct Option: (d)