Each problem consists of three statements. Based on the first two statements,…

Concept

A categorical syllogism combines two statements about groups to test whether a third statement must follow. The key rule here is the subset (containment) rule: if every member of group A belongs to group B (“All A are B”), then any member that is identified as belonging to A -- no matter how it is otherwise labelled -- automatically belongs to B as well. Nothing more is needed to fix that member's membership in B.

Application

1. Statement 1 fixes the whole group “trees in the park” as a subset of “flowering trees”: every tree located in the park is a flowering tree.

2. Statement 2 tells us that dogwoods exist among the trees in the park -- so any tree that is a “dogwood in the park” is, by definition, one of the trees covered by statement 1.

3. Because every tree in the park is a flowering tree (statement 1), and a dogwood in the park is one of those park trees, that dogwood must also be a flowering tree.

4. This holds for every dogwood located in the park, so the third statement -- “all dogwoods in the park are flowering trees” -- is a necessary logical consequence of the first two statements.

Cross-check

Try to build a counter-example: a dogwood inside the park that is NOT a flowering tree. Statement 1 already rules this out, because it declares every tree inside the park -- with no exception -- to be a flowering tree. Since no such counter-example can exist, the third statement cannot be false or left open; it follows with certainty from the given statements.