Take the statements below to be true, even if they differ from known facts. Which of the conclusions follow logically from them?
Statements:
1. No mirror is a frame.
2. All windows are frames.
3. All windows are panels.
Conclusions:
I. Some panels are not mirrors.
II. Some mirrors are panels.
III. No mirror is a panel.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Only conclusion I and either conclusion II or conclusion III follow
A conclusion follows only if it is true in every diagram that fits the statements; each class named in a statement is taken to have members. When two conclusions do not follow on their own, but in every diagram exactly one of them is true, they count as “either one or the other follows”.
“No mirror is a frame”: the circles of mirrors and frames do not touch
“All windows are frames”: the circle of windows lies inside the circle of frames
“All windows are panels”: the circle of windows also lies inside the circle of panels; the panels outside the frames may or may not meet the mirrors
Conclusion I: Some panels are not mirrors. — Follows. The windows are panels; they are also frames, and no frame is a mirror; so these panels are not mirrors.
Conclusion II: Some mirrors are panels. — Does not follow on its own. In case 2 the mirrors and panels do not meet, so it is false there.
Conclusion III: No mirror is a panel. — Does not follow on its own. In case 1 some mirrors meet the panels outside the frames, so it is false there.
Mirrors and panels either meet or they do not; there is no third case. So exactly one of II and III is always true: conclusion I follows, and either conclusion II or conclusion III follows.