Question

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 singers but not dancers are represented by?

• A. R
• B. P
• C. S
• D. T

Hint:

Look for the region that lies inside both the College Students and the Singers shapes but stays completely outside the Dancers shape.

Answer 1

The Correct Option is C

Step 1: Read what each labelled region stands for.
The diagram has three overlapping rectangles: College Students, Singers and Dancers. Region P is College Students only. Region S is where College Students overlaps Singers alone, meaning college student and singer, not dancer. Region R is where College Students overlaps Dancers alone, meaning college student and dancer, not singer. Region T lies inside all three rectangles, meaning college student, singer and dancer together. Regions Q, U and V lie outside the College Students rectangle altogether.

Step 2: Translate the question into set language.
We want college students who sing but do not dance. This needs three things at once: inside College Students, inside Singers, and outside Dancers.

Step 3: Test each option.
Region R is college student and dancer, with no singing, which is the reverse of what we need, so it fails. Region P is college student only, with no singing at all, so it fails the "singer" condition. Region T is college student, singer and dancer together, so it fails the "not a dancer" condition. Region S is exactly college student and singer, with no dancing, satisfying all three conditions together.

Final Answer:
College students who are singers but not dancers are represented by S. \[ \boxed{S} \]