In each of the following questions two statements are given, and these…

Concept. Syllogism reasoning permits two kinds of inference. A mediate inference chains the premises: if class A lies wholly inside class B, and class B lies wholly inside class C, then class A lies wholly inside class C. An immediate inference, called conversion, turns a universal affirmative around: from “All A are B” we obtain “Some B are A”, because the members of A are themselves members of B, so a part of B consists of A. Competitive-exam syllogism is set in the classical convention, in which the subject class named by a premise is taken to be non-empty, and conversion of this kind is therefore valid.

Application to the given premises.

1. The premise “All the pencils are pens” places the pencil class wholly inside the pen class, and the premise “All the pens are inks” places the pen class wholly inside the ink class.

2. Chaining the two by mediate inference gives pencils ⊂ pens ⊂ inks, so every pencil is an ink. That is exactly conclusion (1), “All the pencils are inks.”

3. Converting that derived universal by immediate inference gives “Some inks are pencils”, because the pencil class is a non-empty part of the ink class. That is exactly conclusion (2), “Some inks are pencils.”

Cross-check with nested circles. Draw the pencil circle inside the pen circle and the pen circle inside the ink circle, which is the only arrangement the two premises allow. Every point of the pencil circle then lies inside the ink circle, forcing conclusion (1); and the pencil circle is itself a region of the ink circle, so a part of the ink circle is pencils, forcing conclusion (2). No premise-consistent arrangement breaks either one.

Contrast with the other response forms.

• An either-or response is the form used when the premises settle one of two conclusions as true and the other as false without determining which. Here neither conclusion rests on an unsettled possibility, so that form does not arise.

• A neither-nor response would require the premise chain to leave the pencil-to-ink relation untouched, but the chain fixes it completely.

• A response admitting the particular conclusion alone would discard the transitive chain that produces the universal conclusion.

Result. Both numbered conclusions follow from the premise pair, so the response “Both (1) and (2) follow” is the answer.

A note on convention. Under strict modern predicate logic a universal statement carries no existential import, so “All the pencils are inks” would not by itself guarantee that any pencil exists, and conclusion (2) would not be entailed; the result would then be that only conclusion (1) follows, which is not among the responses offered here. Competitive-exam syllogism follows the classical convention with existential import, under which conversion is valid, and that is the convention this question is set in.