This question concerns the following subsets of R²:A = {(x, y) = R² : (x + 1)² + y² ≤ 4},B = {(x, y) = R² :y> -2x},C = {(x, y) = R² : y ≥ (x − 1)²}.(a)Sketch, on separate diagrams, the sets A, B, AUB and B - A.(b) Prove that C is a proper subset of B.

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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1.1)

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This question concerns the following subsets of R²: A = {(x, y) = R² : (x + 1)² + y² ≤ 4}, B = {(x, y) = R² :y> −2x}, C = {(x, y) = R²: y ≥ (x − 1)²}. (a) Sketch, on separate diagrams, the sets A, B, AUB and B-A. (b) Prove that C is a proper subset of B.