EXAMPLE 2.1.24

Suppose the marked diagram below conveys information about relationships between pirates, ruffians and scoundrels. We use shading to indicate that a region contains no elements. An “X” in a region indicates the existence of at least one element; an “X” on the boundary between two regions indicates that the union of those two regions contains at least one element. If a region is unmarked, then whether that region contains any elements is uncertain. Select the choice that must be true according to the marked diagram.

A. No pirates are ruffians and some ruffians aren’t scoundrels.

B. No pirates are ruffians and some scoundrels aren’t ruffians.

C. All pirates are ruffians and some ruffians aren’t scoundrels.

D. All pirates are ruffians and some scoundrels aren’t ruffians.

E. None of these is correct.

SOLUTION

Combining the observations above, we see that the correct choice is “D. All pirates are ruffians and some scoundrels aren’t ruffians.”