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 dancers but not singers are represented by?
Show Hint
Look for the region that lies inside both the College Students and the Dancers shapes but stays completely outside the Singers shape.
The picture places three groups, College Students, Singers and Dancers, as overlapping rectangles, and each of the seven inner boxes stands for a different combination of these three groups. The question asks for college students who dance but do not sing, so we can check each option in turn instead of deriving the region from scratch.
S: this box sits where College Students and Singers overlap, with no link to Dancers at all, so anyone in S sings but does not dance, the opposite of what we want.
R: this box sits where College Students and Dancers overlap, and it has no connection to the Singers rectangle, so everyone here is a college student, dances, and does not sing. This matches the question exactly.
T: this is the central box shared by all three rectangles, so anyone here sings as well as dances, which breaks the "not a singer" condition.
P: this box is the part of College Students that does not touch Singers or Dancers at all, so nobody here dances, which breaks the "dancer" condition.
Only region R satisfies being a college student, being a dancer, and not being a singer, all at the same time.
Let's summarize:
S and T both involve singing, so they are eliminated.
P involves no dancing at all, so it is eliminated too.
R is the college student and dancer overlap with no singing link, which is exactly what the question asks for.
So college students who are dancers but not singers are represented by R.
