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

Concept: A conclusion follows from a set of categorical statements only when it is true in every arrangement of the classes that satisfies all the statements; one consistent arrangement in which it fails is enough to reject it. Two rules settle such items. First, a universal chain: if the whole of class A lies inside class B and the whole of B lies inside C, then the whole of A lies inside C, and because a named class is taken to be non-empty, this also guarantees that some C are A. Second, a particular statement of the form “Some X are Y” guarantees only that an overlap exists somewhere, so on its own it can never force a universal claim about a third class.

Application to the given statements:

1. “All Turquoise are Beige” places the whole Turquoise class inside Beige.

2. “All Beige are Pink” places the whole Beige class inside Pink, so chaining the two universals puts the whole Turquoise class inside Pink.

3. Turquoise is a non-empty class, so at least one Pink item is Turquoise. “Some Pink are Turquoise” therefore holds in every arrangement that satisfies the statements, so it follows.

4. “Some Pink are Maroon” fixes only that Pink and Maroon overlap somewhere; it says nothing about where that overlap sits, so it cannot force the universal claim “All Beige are Maroon”.

Cross-check with a counter-arrangement:

• Let Turquoise = {t}, Beige = {t, b}, Pink = {t, b, m} and Maroon = {m}. Every Turquoise item is Beige, every Beige item is Pink, and m is both Pink and Maroon, so all three statements hold.

• In this arrangement b is Beige but not Maroon, so “All Beige are Maroon” is false; t is both Pink and Turquoise, so “Some Pink are Turquoise” is true. One such arrangement is enough to reject the first conclusion, and no arrangement can defeat the second because the chain already proves it.

Hence only conclusion (II), “Some Pink are Turquoise”, logically follows from the statements.