Syllogism — Books, calculators, and mobiles (reading “some” correctly): Statements: (a) Some books are mobiles. (b) Some calculators are mobiles. Conclusions to test: I. Some mobiles are calculators. II. Some mobiles are books.

Introduction / Context:This is a straightforward test of interpreting “some” statements. Each premise explicitly asserts a non-empty overlap with the class “mobiles.”

Given Data / Assumptions:

• ∃ (Book ∩ Mobile).
• ∃ (Calculator ∩ Mobile).

Concept / Approach:From the premises themselves we can restate the conclusions: “Some mobiles are books” is equivalent to “Some books are mobiles,” and “Some mobiles are calculators” is equivalent to “Some calculators are mobiles.” Both must be true.

Step-by-Step:1) Use premise (a) to assert existence of at least one entity that is both Book and Mobile → conclusion II.2) Use premise (b) to assert existence of at least one entity that is both Calculator and Mobile → conclusion I.

Verification:A Venn diagram with Mobile as the central set and two overlapping “pockets” for Books and Calculators satisfies both conclusions immediately.

Common Pitfalls:Overthinking “some” as implying additional relations between Books and Calculators; none are needed for these conclusions.

Final Answer:Both conclusions I and II follow.