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Question:

If A = {(x, y): x² + y² ≤ 1; x, y ∈ R} and B = {(x, y): x² + y² ≥ 4; x, y ∈ R}, then A - B = φ, B - A = φ, A ∩ B ≠ φ, A ∩ B = φ

A - B = φ

A ∩ B ≠ φ

B - A = φ

A ∩ B = φ

Solution:

A is the set of all points on or inside the inner circle x² + y² = 1. B is the set of all points on or outside the outer circle x² + y² = 4.
∴ A - B = A, B - A = B, A ∩ B = φ.