. Are the following sets equal? M = {x ∈ Z+: 5 ≤ x < 10} and N = {9,8,7,6}, where Z+ denotes the set of all positive integers. Justify your answer.

Q: Which of the following sets are finite or infinite(i) The set of months of a year(ii) {1, 2, 3, . .…

A:

Q: 8. Give an example of each of the following : (a) a set which is a nbd. of each of its points, (b) a…

A: (b). We consider the example of a set which is not a nbd. of any of its points.

Q: r the closed interval In that each I, contains In+1. Is it true that there exists an element that…

A: In = [an, bn] Also given that  In+1 ⊂ In.

Q: 8. Give an example of each oj the following : (a) a set which is a nbd. of each of its points, (b) a…

A: (b). We given the example of a set which is not a nbd. of any of its points

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

A:

Q: Recall that P(n, r) is the number of r-permutations of an n-element set. Prove the following…

A:

Q: 2. Determine the cardinality of the following sets. (a) {2x :1<x < 16} (b) {N} (c) {0,2 – 1, V4, ø,…

A:

Q: Consider the following families of sets indexed by the set of natural numbers. Which among these is…

A: Given: Intersection or union of a family of sets. To find: Which of the intersection or union of a…

Q: 1. Which of the following statements is correct for any sets A and If “yes", give a proof; if "no",…

A: For any two sets A and B, two statements are given by a A∩Ac∪B⊆B and b A∪B=A \ B. The objective is…

Q: consider the following sets, with U = N; that is, the universal set is the set of natural numbers: A…

A: Given that, C = {1, 3, 5, 7, 9, 11, 13, ............... }

Q: consider the following sets, with U = N; that is, the universal set is the set of natural numbers:…

A: Given B=x|x=n2, 1&lt;n&lt;5

Q: 8. Give an example of each of the following (a) a set which is a nbd. of each of its points, (b) a…

A:

Q: Classify the following sets as finite or infinite. a.) = the set of real numbers less than 5 %3! b.)…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: State which of the following sets are finite or infinite :(i) {x : x ∈ N and (x – 1) (x –2) = 0}(ii)…

A: (i)  (x-1)(x-2)=0 x=1,2 {x : x ∈ N and (x – 1) (x –2) = 0} = {1,2} So, this is a finite set   (ii)…

Q: 1. Find the sup and inf of the following sets. {1/n :n e N} • {2 – 1/n :n € N}. • {e";r € Q}.

A: Supremum: Greatest member of a set, if it exist, is the supremum of the set. Infimum: Smallest…

Q: 2. Enumerate (i.e. list) the members of the following sets: a. {z |z is odd positive integer and z <…

A:

Q: Q 3 Prove or disprove each of the following: For all sets A, B and C, (а) (А — В) — О%3 (А- С) — В

A:

Q: Identify the type of set (finite, infinite or empty) as described by the following: 1. A = {stars in…

A: A set is said to be finite if it contains only finite number of elements. A set is said to be…

Q: . How many relations are there on the set S = {2, 4, 6}? 892 512 none of these 1024

A:

Q: Which of the following pairs of sets is a disjoint set? O (1,2,3,4) and (x x is a natural number and…

A:

Q: Let N be a set of natural numbers. What is a counterexample of the universal statement below? Vx E…

A: Given universal statement,  ∀ x ∈ N, (1/x) &lt; x Where 'N' is a set of natural numbers.  To give a…

Q: 8. Give an example of each oj the following (a) a set which is a nbd. of each of its points, (b) a…

A: We find an example of the given statement

Q: 8. Give an example of each of the following : (a) a set which is a nbd. of each of its points, (b) a…

A: (b) Given the example of a set which is not a nbd. of any of its points

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

A:

Q: 4. Let D (d,}neN be a set of real numbers satisfying d,41 2 d, +1 for all ne N. Prove that D is an…

A: Let D = { dn }n in N  be a set of real numbers satisfying dn+1 &gt;_ dn + 1 for all n in N. Then, we…

Q: Decide which of the following represent true statements aboutthe nature of sets. For any that are…

A: Given information:A1, A2, A3..... are finite and none empty sets.It is also given that…

Q: Define sets A and B as follows: A = {n €Z|n= 8r - 3 for some integer r} and B = {m €Z|m = 4s + 1 for…

A:

Q: 13. The following are empty sets except A. {} B. {x:x € N, x + 999,999 = 999,999} C. {x:x is a whole…

A: Answer (13) We have to check which set is non empty  (A) {}  It is an empty set

Q: Suppose that the universal set U = { 1,2,3,... 20 } and that sets S and T are defined as follows: 1.…

A:

Q: Given the set The B= (– 4,7]N ( –1, 10) – {7}· supremum of B is

A: Introduction: In mathematical analysis, the infimum and supremum are concepts that generalize the…

Q: Prove that the following 2 sets are equal: {4k + 5 : k ∈ Z} = {4k + 1 : k ∈ Z}.

A: Two sets are equal if and only if They have the same element  We are using here if x €A. &lt;=&gt;…

Q: Express the following sets as either an interval, a union of intervals, a finite set, or the empty…

A: Given Sets S, T, U, W To express them as either an interval, a union of interval, a finite set, or…

Q: 1) If a and b are given integers, not both zero,show that the set T {ax+by: x,y are integers} is the…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Which of the following sets are uncountable? The set of reals R The set of rationals Q The set of…

A:

Q: Define sets A and B as: : {n E Z\n = 4r + 3 for some integer r}. • B= {m E Z m = 4s – 1 for some…

A: the objective is to solve the above questions.

Q: Are there numbers a and b such that |a + b| &gt; |a|+|b|?

A:

Q: Which of the following pairs of sets are disjoint(i) {1, 2, 3, 4} and {x : x is a natural number and…

A: Two sets are said to be disjoint set if they have no element in common We have two sets {1, 2, 3, 4}…

Q: The supremum of the set S={1- (-1)". :neN is a) 1 b) 0 c) п d) 2

A: The given set is  S=1--1nn:n∈ℕ The elements of the set can be listed by putting different values of…

Q: Decide if the following statements about suprema and infimaare true or false. Give a short proof for…

A: Given that sup A&lt;inf B for two nonempty sets A and B. Its is known that in between any two…

Q: (3.2) Indicate which of the following sets are compact in X. (a) C = {4,n € N}, X = R (b) C = Qn (0,…

A:

Q: which of the following is true for every n belongs to N (natural number set)? Select one: A. (xy)" =…

A: (xy)n=xnyn is true.

Q: Given the sets ((A n D)U (Bn C)) and (((An D) U B)nc): 4. Determine which one is a subset of the…

A: Given two sets  A∩D∪B∩C and A∩D∪B∩C Note: We will use the following definitions of union and…

Q: If X and Y are any sets, which of the following exactly expresses what it means for XSY to be false?…

A:

Q: Which of the following sets is open in (IR, Tu)? OR-(Q-Z) (1)"2n? nin?:nE N} R - [2,5) O 12, 5) U…

A:

Q: Which of the following sets are closed under subtraction? O The set of all whole numbers. O {0,1} O…

A: Option B Because if you will take any number between zero and one and you will get the difference…

Q: Let n and r be non-negative integers such that r <n. Then, C + "C , = **C,

A: nCr=n!r!(n-r)!

Q: Is it true that, if S is a nonempty set of positive real numbers, then 0<=inf S?

A:

Q: 1. Determine whether the following sets are finite or infinite. Indicate your choice by writing…

A:

Q: Let, x belongs to positive integers. A, B and C are the sets expressed with the following set buile…

A: Given: A={x|x is a prime number not exceeding 15} B={x|x is a positive odd integer not exceeding 15}…

Q: Consider the set N of positive integers to be the universal set. Sets H, T, E, and P are defined to…

A: Let H' denote the complement of H and T' denote the complement of T Two sets are said to be disjoint…