RAS question
Which Venn diagram best represents the relationship among: Teachers, Graduates, Singers?
Correct answer: (D) Three mutually overlapping circles.
The relationship among Teachers, Graduates and Singers is best represented by three mutually overlapping circles, because the three sets can share members without any one set being wholly contained in another.
Explanation
NCERT explains that Venn diagrams represent relationships between sets through closed curves, usually circles, and that intersection marks elements common to sets. Here, the three groups are independent social categories: a teacher may or may not be a graduate, and a singer may or may not be a teacher or a graduate. So the diagram must allow common members, such as someone who belongs to two or even all three sets, while also allowing members who belong to only one set. Since none of Teachers, Graduates and Singers is a subset of another, the correct representation is three mutually overlapping circles, not separate circles or nested circles.
Why the other options are wrong
- (A) Three separate non-overlapping circles would show the sets as disjoint, but teachers, graduates and singers can have common members.
- (B) Putting Teachers wholly inside Graduates wrongly makes every teacher a graduate and also wrongly keeps Singers separate from both other sets.
- (C) Putting Graduates inside Teachers and Singers inside Graduates creates a chain of subsets, but none of the three sets is fully inside another.
Concept
This tests set relationships and Venn diagram selection, a recurring RAS reasoning task because candidates must distinguish overlap, disjointness and subset containment from ordinary category descriptions.