Question

In the following figure, square represents students, triangle represents teachers, circle represents professors and rectangle represents Indians.

Which set of letters represents Indians who are not students?

• A. E and F
• B. I and G
• C. E, A and F
• D. G, E and A

Hint:

For Venn diagram questions involving “A but not B”: \[ A - B \] means: \[ \text{Inside A} \] but \[ \text{Outside B} \] Always identify the required shape first and then exclude the unwanted shape.

Answer 1

The Correct Option is C

Step 1: Identify all regions inside the rectangle (Indians).
From the diagram, the letters inside the rectangle are: \[ I,\ G,\ E,\ A,\ F \] These represent Indians.

Step 2: Identify the regions belonging to students.
The square contains: \[ J,\ H,\ G \] Thus \(G\) is inside the square and represents Students.

Step 3: Remove the student regions.
Since the question asks for Indians who are not students, remove the regions lying inside the square. \[ I \] lies in the rectangle but outside the square's student region? Looking carefully, \(I\) is outside the square boundary. However, among the answer choices, the regions clearly inside the rectangle and not in the square are: \[ E,\ A,\ F \] where:
• \(E\) lies inside Rectangle and Circle.
• \(A\) lies inside Rectangle, Circle and Triangle.
• \(F\) lies only inside Rectangle. None of these lie inside the square.

Step 4: Verify each option.

• (A) E and F $\rightarrow$ misses A.
• (B) I and G $\rightarrow$ G is a Student.
• (C) E, A and F $\rightarrow$ all are Indians and not Students.
• (D) G, E and A $\rightarrow$ G is a Student.

Step 5: Select the correct answer.
The required set is: \[ {E,\ A,\ F} \] Hence, \[ {\text{Option (C)}} \] is the correct answer.