Which of the following subsets of G CC are (i) open, (ii) connected, (iii) a domain? (a) G = {z € C; |z| < 2} \ {z € C; Rez = 0}, (b) G = {z € C; |2| < 2} n{z € C; Re z > 0}, (c) G = {z € C; |2| < 2} U {z € C; Re z > 0}, (d) G = {z € C; |2| < 2} \ {z € C; Re z = 0}. %3D

Q: 4. (a) If X is an infinite dimensional space, show that the set {x = x | || x || = 1} is not…

A:

Q: 1. Let S = {1,2, 3, 4}. (a) How many relations are there on S? (b) How many are reflexive? (o) How m…

A:

Q: Set roster notation of U={r € Z l -2<r<2

A: we have given the set U = {r∈Z,  -2&lt;r&lt;2} we have to write the set roster notation of U The set…

Q: Let A and B be sets. Prove that A ≤ B in each of the following. (i) A = {x²: x € Z} and B = Z (ii) A…

A:

Q: 2. Decide whether each of the following sets are finite, denumerable or uncountable. Explain each of…

A:

Q: (ii) for every singleton set A, m* (A) = 0.

A:

Q: 1 - Let A = {x € R: -2-4<x<5+0} B = {x € R: x²(x+y+1)x < 0} Find the set AUB,ANB, A\B, B\A A', B' as…

A:

Q: Theorem 9. The following statements regarding the set E are equivalent: (i) E is measurable. (ii)…

A:

Q: 10. Determine whether each of these functions from {a, b, c, d} to itself is one-to-one. a) f(a) =…

A:

Q: 2] [ State the Sequential Criterion Theorem.

A:

Q: 1. Find all regular points of the set : {x € Rª | 2(x1+x2+x3)³ +3(x1+x2+x3)² = 1, x²+x²+x²+x4 = 1}.

A: The given set is: x∈R4|2(x1+x2+x3)3+3(x1+x2+x3)3=1,x12+x22+x32+x4=1

Q: 1. Find the sets of interior points and boundary points of each set and classify the set as open,…

A:

Q: . Sketch the graph of the set defined by A x B where A is the closed interval [-2, 4] and B = {1, 3,…

A:

Q: Let (A,) be a poset. Define a function f: A → P(A) by f(x) = {a € A: a <x}. What can you say about x…

A: Here given that be a poset.Define function is  by Noted that here  is power set of  .Here we have to…

Q: Show: P(EG) ≤ P(F|G₂) = P(E) ≤ P(F), given that E, F, G₁, G2,.., G

A:

Q: 7. Sketch the set {(x, y) = R² : ||(x, y) || = 1} when: (a) ||(x, y)=√√√x² + y² (b) ||(x, y) || =…

A:

Q: 6. Let 2 be a set and f, g: → R. Assume max{f(x) + g(x) | x = }, max{f(x) |x€N}, and max{g(x) | x =…

A:

Q: Determine (without proof) the suprema and infima of the following sets: (a) {n € N : n² < 10} (b)…

A:

Q: (A) If A = {x E R: – 1<x< 2}, B = {x € R: 0 < x < 1}, C = {x € R: 1< x < 2}, The sketch the graph of…

A: That's easy, have a look.  Have a great day!!!

Q: Given a finite set S, find all possible values of |S] so that the set {(a, b) | (a E S) A (b e S) ^…

A:

Q: (a) What is the cardinality of the interval (0, 1), finite, countably infinite, or uncountable? (b)…

A:

Q: Prove that the set B = {r € Q: 1² < 20 or r < 0o} is a cut.

A: In this question, we have to prove that the set,  B = x∈ℚ : x2 &lt; 2 or x &lt; 0 is a cut.

Q: :-(-1)" : n € N. State without proof the values of inf D (a) (i) Consider the set D = and sup D.…

A: As per the guidelines I am answering the only the part (a) of the question. For rest questions…

Q: 1- Find the set of lower bounds and the set of upper bounds of the following sets in R, if it…

A: Since you have posted multiple sunparts of a question so according to our guidelines we will solve…

Q: 13. (9 points) Let D be the set of finite subsets of positive integers. Let S be the set of all…

A: The objective of this question is to find the set of all even factors of given numbers using the…

Q: Let X={x=(x1, x2, X3, X4) : Xi E {1,2,3,4,5,6,7,8,9,10,11,12} for i=1,2,3,4 such that x1 < x2 < X3 <…

A: Given:X={x=x1, x2, x3, x4 : xi∈1,2,3,4,5,6,7,8,9,10,11,12for i=1,2,3,4 such that…

Q: (a) By contradiction, prove that V r, y € Z, if ry is even and y is odd then x is even. (b) Show…

A: (a) Given v x,y ∈Z,     &amp; xy is an even integer with y is odd.     To show x is even.      Let…

Q: (2.1) Let b> 0 and X [-b, b). Here we admit %3D B"open" in r if and only if (0} B or (-b, b) C B.…

A:

Q: 3. Find if each of the following sets or open, closed, both open and closed, or neither open nor…

A: A set X in R is open if and only if for every x∈X there exists some ε&gt;0 such that (x−ϵ,x+ϵ) is a…

Q: Let B = {((-1)n*n)/(n+1) : n = 1, 2, 3…}. Find the limit points of B. Is B a closed set? Is B an…

A:

Q: 6.3. Let (A, <A) and (B,<B) be two partially ordered sets. One can define on the cartesian product A…

A: Given: A, ⩽A and B, ⩽B are partially ordered sets.  A Cartesian product A x B is defined with…

Q: span (EE-EE) 3 O 2 O (A) and (B) O (A) ... = span Neither (A) nor (B). (B)... = span (4-6-8) 2 3 2 5…

A: Given that, span121, 031, 004, 152 We have to find the equivalent spanning set.

Q: Which characteristic/s implies(y) that a set S of real numbers is closed? S has no accumulation…

A: To choose correct option from given question.

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.