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(a) Give the centre c and the radius r of S = B(0,5) B(3, 4). (b) Which of the following are neither open nor closed subsets of Y = (0,7]. V₁ = (0,2], V₂ = [5,7), V3 = (4,7], V₁ = (3,6], V = (2,17/2). (c) Let M = R. Using interval notation, give a simplified expression for the set L = [B(3, 1) UB(7,1)] n B(5,2).

(a) Give the centre c and the radius r of S = B(0,5) B(3, 4). (b) Which of the following are neither open nor closed subsets of Y = (0,7]. V₁ = (0,2], V₂ = [5,7), V3 = (4,7], V₁ = (3,6], V = (2,17/2). (c) Let M = R. Using interval notation, give a simplified expression for the set L = [B(3, 1) UB(7,1)] n B(5,2).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 10E
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please do a) , b) and c)

(a) Give the centre e and the radius r of S = B(0,5) B(3, 4). (b) Which of the following are neither open nor closed subsets of Y = (0,7]. V₁ = (0,2], V₂ = [5,7), V3 = (4, 7], V₁ = (3,6], V₁ = (2,17/2). (c) Let M = R. Using interval notation, give a simplified expression for the set L = [B(3, 1) UB(7,1)] n B(5,2). (d) Let (F₂) be a sequence of closed subsets of M, and S; (j = 1,...,5) be subsets of M such that. S₁ F S₂ = U_Fn S3 = Sg. NEN* TEN. Also, S4 has a boundary point a such that a € S, and every convergent sequence in S5 has its limit in S5. Which of the sets S₁,..., S5 are closed. (f) Let F = {x € R: x - 3| < 7 and x + 1 ≥ 2}. Give explicitly F, and F (g) Let An = [2 + (−1)”+7, 5 + (−1)”+4), n = N*. Set B₂ = An B (e) Let u = (2, 2), o = = (0,0) be points in M = R². Let P = (1,6) be a point lying on S(u, 1) and on the boundary of B(0,r) in R2, for some r > 0. Independently of b, give a numeric value for r. An+1. Give explicitly An, Bn, and (h) Suppose that (M, d) is a discrete metric space and a € M. Give a simplified and explicit expression for: E₁ = B(a, 1/3), E2 = B(a, 1/3), E3 = [S(a, 1)]º, and E4 = S(a, 1). (i) Give the formal definition in terms of 8 and of the continuity of f: M→ M at ro € M. (j) Suppose that (M, d) is a discrete metric space. Give the general form of a convergent sequence (an) in M whose limit is 2.
Transcribed Image Text:(a) Give the centre e and the radius r of S = B(0,5) B(3, 4). (b) Which of the following are neither open nor closed subsets of Y = (0,7]. V₁ = (0,2], V₂ = [5,7), V3 = (4, 7], V₁ = (3,6], V₁ = (2,17/2). (c) Let M = R. Using interval notation, give a simplified expression for the set L = [B(3, 1) UB(7,1)] n B(5,2). (d) Let (F₂) be a sequence of closed subsets of M, and S; (j = 1,...,5) be subsets of M such that. S₁ F S₂ = U_Fn S3 = Sg. NEN* TEN. Also, S4 has a boundary point a such that a € S, and every convergent sequence in S5 has its limit in S5. Which of the sets S₁,..., S5 are closed. (f) Let F = {x € R: x - 3| < 7 and x + 1 ≥ 2}. Give explicitly F, and F (g) Let An = [2 + (−1)”+7, 5 + (−1)”+4), n = N*. Set B₂ = An B (e) Let u = (2, 2), o = = (0,0) be points in M = R². Let P = (1,6) be a point lying on S(u, 1) and on the boundary of B(0,r) in R2, for some r > 0. Independently of b, give a numeric value for r. An+1. Give explicitly An, Bn, and (h) Suppose that (M, d) is a discrete metric space and a € M. Give a simplified and explicit expression for: E₁ = B(a, 1/3), E2 = B(a, 1/3), E3 = [S(a, 1)]º, and E4 = S(a, 1). (i) Give the formal definition in terms of 8 and of the continuity of f: M→ M at ro € M. (j) Suppose that (M, d) is a discrete metric space. Give the general form of a convergent sequence (an) in M whose limit is 2.
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