6. Analyze whether the following sets are convex: Please make the answers step by step as explicit as possible. thank youa) A = {(x, y) ∈ R2 : y ≥ x2}b) B = {x, y) ∈ R2 : y ≥ |x|}c) C = {x, y) ∈ R2 : x2 + 3y2 ≤ xy + 5}d) D = {(x, y, z) ∈ R3 : x + y = 2; z = 5}e) A ∩ Bf ) C1 = {(x, y, z) ∈ R3 : 2x − 5 + z ≤ 5, x < 16}.g) C2={(x,y,z,w)∈R4:x−3y=x+2w}.h) C3={(x,y)∈R2:x2+y2≤16}.i ) C4={(x,y)∈R2:2xy−x2−y2≥4}.

A.Let (x1, y1) and (x2, y2) be two points in A, where y1 ≥ x1^2 and y2 ≥ x2^2.Consider any point on…

Answered: 6. Analyze whether the following sets…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.7: Distinguishable Permutations And Combinations

Problem 29E

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6. Analyze whether the following sets are convex: Please make the answers step by step as explicit as possible. thank you

a) A = {(x, y) ∈ R² : y ≥ x²}
b) B = {x, y) ∈ R² : y ≥ |x|}
c) C = {x, y) ∈ R² : x² + 3y² ≤ xy + 5}
d) D = {(x, y, z) ∈ R³ : x + y = 2; z = 5}
e) A ∩ B
f ) C₁ = {(x, y, z) ∈ R³ : 2x − 5 + z ≤ 5, x < 16}.
g) C₂={(x,y,z,w)∈R⁴:x−3y=x+2w}.
h) C₃={(x,y)∈R²:x²+y²≤16}.
i ) C₄={(x,y)∈R²:2xy−x²−y²≥4}.