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

Two rules govern which conclusions validly follow a chain of categorical statements. First, chaining "All A are B" with "All B are C" forces every A into C as well, so "All A are C" is a definite, always-valid conclusion — this works because B, being the subject of the second (universal) statement, is fully distributed there, and combined with the first statement placing every A inside B, every A is thereby carried into C. Second, a definite particular conclusion between two end terms requires their shared middle term to be distributed in at least one of the two statements linking them. A universal affirmative statement distributes only its subject, never its predicate, and a particular ("some") statement distributes neither of its terms; so if the middle term appears only as the predicate of a universal statement and as the subject of a "some" statement, it stays undistributed throughout, and no definite link between the end terms can be forced — such a conclusion is only possible, never certain (the fallacy of the undistributed middle).

1. "All jugs are kings" and "All kings are balms" chain through the middle term "kings", which is the subject of the second, universal, statement and therefore fully distributed there; this forces every jug into balms, so "All jugs are balms" is fixed as definitely true — conclusion (I) follows.

2. To test conclusion (II), the derived statement "All jugs are balms" and the given statement "Some balms are powders" must be combined through their shared term "balms".

3. In "All jugs are balms", balms is the predicate of a universal statement and so is undistributed there; in "Some balms are powders", balms is the subject of a particular statement, which distributes neither of its terms, so balms is undistributed there too.

4. Because the shared term "balms" is undistributed in both statements, nothing forces the powder-balms overlap to touch the jug subset of balms, so "Some powders are jugs" is not fixed as certain — conclusion (II) does not follow (the fallacy of the undistributed middle).

A quick diagram check confirms this: draw balms as a large circle, kings as a smaller circle fully inside it, and jugs as a smaller circle fully inside kings — that placement is forced by the two universal statements. Powders is a separate circle that must overlap balms somewhere ("some balms are powders"), but nothing forces that overlap to touch the small jugs circle; it can sit entirely in the part of balms outside jugs. This confirms conclusion (I) is forced while conclusion (II) is only a possibility.

Only conclusion (I) follows.