Study the diagram below, which shows three overlapping groups, College Students, Singers and Dancers, divided into the labelled regions P, Q, R, S, T, U and V, and answer the question that follows.
College students who are neither dancers nor singers are represented by?
Show Hint
Look for the region that lies inside the College Students shape but stays completely outside both the Singers shape and the Dancers shape.
The diagram overlaps three rectangles, College Students, Singers and Dancers, and each small box represents a specific combination of the three. The question asks for college students who are neither singers nor dancers, so every choice can be checked against the picture.
S: this box is College Students overlapping Singers, so anyone here sings, which breaks the "neither" condition right away.
V: this box sits inside the Dancers rectangle but completely outside the College Students rectangle, so it describes a dancer who is not a college student at all, not a "college student who does not dance". It cannot answer a question about college students.
Q: by the same reasoning, this box sits inside the Singers rectangle but completely outside the College Students rectangle, so it describes a singer who is not a college student, again not something that can answer a question restricted to college students.
P: this box is the part of College Students that does not touch Singers or Dancers at all, so it is exactly a college student who neither sings nor dances.
Region P is the only one that is genuinely inside College Students while being outside both other groups, so it is the correct region. Note that some printed answer keys for this question mark option (d), Q, but that region lies outside the College Students boundary in the diagram itself, the same way V is outside it and is correctly ruled out as the answer to the dancers-and-singers question. Using the diagram consistently, the same way it correctly gives R, S and T for the earlier three questions, points to P here.
Let's summarize:
S involves singing, so it is ruled out.
Q and V both sit outside the College Students rectangle, so neither can describe a college student at all.
P is the college-student-only region, matching "neither a singer nor a dancer" exactly.
So college students who are neither dancers nor singers are represented by P.
