Statements: All the phones are scales. All the scales are calculators.…

Concept

In categorical syllogism reasoning (the standard convention used for these statement-and-conclusion questions), every universal statement carries existential import — it is treated as asserting that its subject category actually has members. Under this convention, a subset chain (‘All A are B’, ‘All B are C’) can be combined directly — chaining the two links gives ‘All A are C’ — but neither link may be reversed on its own (‘All B are C’ does not give ‘All C are B’). A separate, standard immediate-inference rule — conversion of a universal statement — lets ‘All X are Y’ convert to the weaker particular form ‘Some Y are X’; this conversion-by-limitation is a fixed rule of the system, not a case-by-case assumption.

Step-by-step application

1. Let P = phones, S = scales, C = calculators. Statement 1 gives P ⊆ S (every phone is a scale); statement 2 gives S ⊆ C (every scale is a calculator).

2. Chain the two subset links: P ⊆ S ⊆ C, so P ⊆ C — every phone is a calculator. This is the direct conclusion obtained by combining the statements in the order given.

3. Because ‘All phones are calculators’ is now established, applying the standard conversion rule for universal statements converts it directly to the particular form: ‘Some calculators are phones.’ This is the fixed immediate-inference rule for universal statements in this reasoning system, not an extra assumption specific to this item.

4. Check the two reversed claims separately. ‘All calculators are scales’ would need C ⊆ S, which statement 2 (S ⊆ C) does not provide — calculators can exist outside the scales group. Likewise ‘All scales are phones’ would need S ⊆ P, which statement 1 (P ⊆ S) does not provide — scales can exist outside the phones group. Neither reversed claim is supported.

Cross-check

A three-circle Venn diagram with the phones circle drawn entirely inside the scales circle, and the scales circle drawn entirely inside the calculators circle, confirms the same reading: the phones circle sits fully inside the calculators circle, and the two circles necessarily overlap by definition, while nothing forces the larger calculators or scales circles to stay inside the smaller circles they contain.

Result

Only the conclusions that follow the stated direction of the chain — together with its automatic particular converse — hold; the two reversed claims do not.

Reference diagram