Read the given statements and conclusions carefully. Assuming that the…

Syllogism conclusions are checked with the standard rules for combining categorical statements: a universal affirmative statement of the form 'All A are B' can be converted to the particular statement 'Some B are A'; and when two universal affirmative statements share the same subject term, they validly yield a particular conclusion linking their two predicates -- 'All A are B' plus 'All A are C' gives both 'Some B are C' and 'Some C are B'. By contrast, a particular statement such as 'Some X are Y' only asserts that some unspecified members of X are Y, so it cannot be safely chained with another statement about a different, also-unspecified subset of the same term.

1. Define the four classes: Sweaters (S), Jackets (J), Trousers (T), Cargoes (C).

2. The statements 'All sweaters are jackets' (S is inside J) and 'All sweaters are trousers' (S is inside T) share the same subject term, sweaters.

3. By the common-subject rule, the same sweater-items sit inside both J and T, so 'Some trousers are jackets' -- Conclusion (II) -- is validly established.

4. The statement 'Some trousers are cargoes' only asserts that an unspecified subset of trousers overlaps with cargoes. Since sweaters are only one subset of trousers, nothing forces the cargo-overlapping trousers to be the same as the sweater-trousers, so 'Some cargoes are sweaters' -- Conclusion (I) -- is not established.

Independent check by diagram: draw the sweaters circle fully inside both the jackets circle and the trousers circle, and draw the trousers-cargoes overlap as a separate region of the trousers circle that does not touch the sweaters circle. This single diagram satisfies all three statements while Conclusion (I) fails, proving (I) is not necessary. No diagram consistent with the statements can avoid a trousers-jackets overlap, since the sweaters circle must always sit inside both, confirming Conclusion (II) always holds. So only Conclusion (II) follows.