Using the exam convention that a diagram should show only the relations…
2010
Using the exam convention that a diagram should show only the relations stated, the two small circles, read from left to right, represent the classes of men and plants, respectively; the large circle represents mortality. Which figure represents the proposition “All men are mortal”?
Attempted by 2 students.
Show answer & explanation
Concept
In a class diagram, the universal affirmative proposition “All A are B” means that every member of class A belongs to class B.
Therefore, the circle for A must lie wholly inside the circle for B. Under the convention used in this item, a third class with no stated relation is drawn separately rather than adding an extra subset or overlap relation.
Application
Let the large circle denote mortality, the left small circle denote men, and the right small circle denote plants.
Because all men are mortal, the entire men circle must lie inside the mortality circle.
The proposition states no relation between plants and mortality, so the plants circle remains separate from the mortality circle in order to show only the stated relation.
Cross-check and contrast
Both small circles outside mortality would exclude men from mortality.
Both small circles inside mortality would add the unstated claim that all plants are mortal.
A plant circle crossing the mortality boundary would add a partial-overlap relation not stated in the proposition.
Hence, the required figure has the men circle wholly inside the mortality circle and the plants circle outside it.