Exams › JEE Main › Maths

Two sets A and B are as under : A = {(a, b) ∈ R × R : |a − 5| < 1 and |b − 5| < 1}; B = {(a, b) ∈ R × R : 4(a − 6)² + 9(b − 5)² ≤ 36}. Then :

1. A ⊂ B
2. A ∩ B = ϕ (an empty set)
3. neither A ⊂ B nor B ⊂ A
4. B ⊂ A

Correct answer: neither A ⊂ B nor B ⊂ A

Solution

The correct option is accurate because set A represents a square region around the point (5, 5), while set B describes an ellipse centered at (6, 5). Since the two shapes do not completely overlap or contain each other, neither set is a subset of the other.

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