A Venn diagram is drawn followed by the four choices. Select the correct choice which represents the given diagram.

Correct — option (1), Teacher, Mother, Doctor.

The figure has three equal circles: two side by side at the top and one below the centre. Every pair of circles overlaps, and all three share a central region. So the matching classes must allow every pair, and all three at once, to have common members.

Teacher, Mother, Doctor fits, because these are roles one person can combine.
A teacher can be a mother.
A doctor can be a mother.
A doctor can also teach, for example in a medical college.
A woman doctor who teaches and has children sits in the centre.

Each role also exists without the others, so the parts outside the overlaps are filled too.

The other options each contain a pair that cannot overlap: a planet is not a star, an income tax is not a sales tax, and a book is not a piece of furniture. Since the figure needs all three pairs to overlap, one impossible pair rules a set out.

The idea to remember: three mutually overlapping circles mean every pair of classes shares members, and all three do too.

Why the others are wrong

• (2)
  Universe, Planets, Stars — Planets and stars both lie within the universe, but a planet is not a star. The matching figure is one large circle with two separate circles inside it.

  The given figure would need Planets and Stars to overlap, and also needs parts of both outside Universe. Neither is possible.

• (3)
  Income Tax, Sales Tax, Service Tax — These are three different taxes. Income tax is levied on income; sales tax on the sale of goods; service tax on services. No single tax is two of these at once.

  The matching figure is three separate circles. The given figure needs every pair to overlap, which these classes cannot.

• (4)
  Library, Books, Furniture — A book is not a piece of furniture, so the Books and Furniture circles cannot overlap.

  Read as a whole and its parts, a library holds books and furniture: one large circle with two separate circles inside, the same shape as option (2). Read as three separate kinds of thing, the circles do not meet at all. Either way, it is not the given figure.

A logical Venn diagram draws each class as a circle, and the way the circles sit shows how the classes relate.

Separate circles: no common member (planets and stars). A circle inside another: one class wholly within the other (Jaipur within Rajasthan). Overlapping circles: some members shared, while each class also has members outside the other (teachers and mothers).

Three mutually overlapping circles make seven regions: three for one class only, three for exactly two classes, and one for all three. To match classes to such a figure, check each pair for a shared member, then check that one member can belong to all three.

Key facts

• Three mutually overlapping circles have seven regions: three for one class only, three for exactly two classes, one for all three.
• Separate circles show classes with no common member; a circle inside another shows one class wholly contained in the other.
• Teacher, Mother and Doctor are roles one person can hold together, so every pair and all three can overlap.
• Universe, Planets, Stars: one large circle holding two separate circles, since no planet is a star.
• Income Tax, Sales Tax, Service Tax: three separate circles, since no tax is two of these at once.

Common traps

• Test every pair, not just one. Universe overlaps both Planets and Stars, but Planets and Stars cannot overlap each other.
• Roles a person holds can overlap; different kinds of object, such as books and furniture, cannot.
• "Mother" limits the Teacher–Mother and Doctor–Mother overlaps to women, but those overlaps still exist. A region needs only some members.

UnlockIAS will link similar questions from RAS Pre 2021 here once that paper is published on this site.

• practice — not a real PYQ

  Which of the following figures best represents the relationship among Animals, Dogs and Cats?

  • (a)Three separate circles
  • (b)One large circle containing two separate circles
  • (c)Three mutually overlapping circles
  • (d)Three circles, one inside another
  Answer(2) — Dogs and cats are both animals, so both circles sit inside Animals, and no dog is a cat, so they do not overlap. Option (1) would put dogs outside animals; option (3) would need a dog that is a cat; option (4) would need all cats to be dogs or all dogs to be cats.
• practice — not a real PYQ

  Which of the following sets is best represented by three circles, one inside another?

  • (a)India, Rajasthan, Jaipur
  • (b)Rajasthan, Gujarat, Punjab
  • (c)Men, Fathers, Teachers
  • (d)Fruits, Mangoes, Vegetables
  Answer(1) — Jaipur lies within Rajasthan, which lies within India. Option (2) names three separate states (separate circles); in option (3), Fathers sits inside Men but Teachers overlaps both; in option (4), Mangoes sits inside Fruits, but Vegetables neither holds Fruits nor sits inside Mangoes.