JEE Main · 2021 · 17 Mar 2021 · Shift 1 · Sets Relations and Functions

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In a school, there are three types of games to be played. Some of the students play two types of games, but none play all the three games. Which Venn diagrams can justify the above statement?

(A)Q and R
(B)None of these
(C)P and R✓ Correct
(D)P and Q

Answer: (C)

Solution

The condition is: some students play exactly two games, and no student plays all three games.

In a Venn diagram:

The central region (intersection of all three sets) must be empty.
At least one of the pairwise-only regions (e.g., $A \cap B$ but not $C$ ) must be non-empty.

Diagrams P and R satisfy these conditions (no central overlap, but pairwise overlaps exist).

Thus the answer is P and R.

JEE Main · 2021 · 17 Mar 2021 · Shift 1 · Single correct option

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