What is the range of the function in set notation? A) −5 ≤ x ≤ 4 B) −3 ≤ x ≤ 4 C) −3 ≤ x ≤ 2 D) −5 ≤ x ≤ 3

Q: Come up with an open interval A and closed interval B such that A U B = (0,4) and A (upside down U…

A:

Q: Give an example to show arbitrary union of open sets is again open. Is the result true for arbitrary…

A:

Q: Let R be the set of all real numbers with the euclidean topology. Show that R has an uncountable…

A: We will first show : (iii) If S is dense in X, then T is dense in X, where S and T are non-empty…

Q: 6. Show that the span of this set is all of R?. {}}

A: Let S=v1,v2,...,vn be a set of vectors in a vector space V(F) . The vector space V is spanned by S,…

Q: Provide a counter example that infinity intersection of open set is open

A:

Q: can two disjoint sets be close? Justify your answer using an example.

A: We know that any closed interval of the form [a,b] is an closed set. We use this fact further.

Q: S is a nonempty set of real numbers that is bounded.

A:

Q: A is a subset of the real numbers, R.

A:

Q: Denote the set using the listing method {x| x is reciprocal of a positive odd number

A: The set of positive odd numbers are as follows: 1,3,5,7,9,11,13,15,17,19,21,23,……… Given a real…

Q: Give an example of numbers x, y such that |x| + |y| = x − y.

A: Given that: give an example of numbers x, y such that |x| + |y| = x − y.

Q: Express the set using the roster method. the set of natural numbers less than or equal to 6.

A: Given: the set of natural numbers less than or equal to 6. To express: The given set in roster…

Q: E is closed. - E is complete, i.

A: It is given that X is a complete metric space and E is a subset of X. We have to prove that the…

Q: Consider the set A = {[a, b] C R : a, b E Q, a < b}, i.e., A is the sets of all non-degenerate…

A:

Q: Give an example of an irrational point in Cantor Set.

A: There are infinitely many irrationals in cantor set ... one example is  ' an number that has base 3…

Q: Let U = (−∞,∞), A = [−1, 6], B = [−6, 2). In interval notation, determine A ∩ B. And in interval…

A:

Q: a Prove that the interval [-1, 2] is a closed set in R. Explain each step in your argument.

A:

Q: Consider the set X = {x € R¹ / 93x₁ +34x2 +26x3 + 18x4 ≤ 131, X1, X2, X3, X4 = {0, 1}}. Show that x₁…

A: (a) It is given that x=x1,x2,x3,x4 such that 93x1+34x2+26x3+18x4≤131 and x1,x2,x3,x4∈0,1. So, the…

Q: Describe the set S = { x : I 1/2x - 3 I &gt; 4} in terms of intervals.

A: S=x : 12x-3&gt;4

Q: What is the width of the class interval of 1-3?

A: Width of the class interval

Q: Describe the set S = x :12 x − 3&gt; 4in terms of intervals

A: Given: S=x:12x-3&gt;4 To Describe: Given set in the intervals.

Q: Describe the set as a union of finite or infinite intervals { X : I 2x + 4 I &gt; 3}

A: Given set is x:2x+4&gt;3

Q: Describe the set as a union of finite or infinite intervals. {x : |x − 4| &gt; 2}

A: can be written as x-4&gt;2 or x-4&lt;-2

Q: Show that the set of irrational numbers is not a closed set.

A:

Q: 3. Using the definition of open sets, prove that an interval (0, a) is open where a > 0 is an…

A: (3) Definition of open sets: To define open set first we define an open ball For a real number x and…

Q: Tet X and Y be infinite sets prove that XUY is infinite

A:

Q: Give an example of a set of numbers that is: a. Closed under both addition and multiplication. b.…

A: a. Set of real numbers b. Set of odd natural  numbers c. Set of irrational numbers

Q: Proving a divisibility relation is transitive

A:

Q: Let R be a total relation on a set of 15 elements. Then the number of ordered pairs in R is equal…

A:

Q: Show that the set of Natural Numbers (N) is a closed set.

A: The objective is to prove that the set of natural numbers is closed. To prove that it is closed we…

Q: Consider a set A with 10 elements.  How many different functions are there from the set A to a set…

A: Introduction: In mathematics, a function is an expression, rule, or law that specifies a…

Q: Let S be a nonempty bounded set containing a sequence of rational numbers. Provide an example such…

A:

Q: Express the set using the Roster Method: {x|x X eN and x)53

A: GIVEN XX∈N and  X&gt;5

Q: Write the interval in set-builder notation. [-4, 1] U [5, ∞0) O {xl-52 x ≥ 1 orx ≤ 4} O {x|-4 ≤ x ≤…

A: Set builder notation is represented as Interval notation, and it is a way to define a set of numbers…

Q: What is the set R of all real numbers?

A: Real numbers are the numbers which include both rational and irrational numbers. A real number is a…

Q: Suppose A and B are two finite sets such that |B| = 2 |A| and the number of relations on A is 16.…

A:

Q: Use set builder notations to prove that:  (a) X ⊕ Y = (X ∪ Y ) − (X ∩ Y ),           (b)(Y −X) ∪ (Z…

A: We have to prove the following using the set builder notation: (a) X⊕Y=(X∪Y)−(X∩Y) (b)…

Q: Prove directly that the union of two disjoint sets, where one is countably infinite and the other is…

A:

Q: In Exercises 23-26, describe the set as a union of finite or infinite intervals. 23. {x : Ix - 41…

A: 23) Given that, x:x-4&gt;2

Q: Express the set of real numbers between but not including 2 and 7 as follows. (a) In set-builder…

A: Set: In set builder notation the real number between 2 and 7 but not including both the numbers, Let…

Q: Let RC R+ x R+ with R = {(x, y)|[x] = [y]}, that is, x and y round up to the sane number.…

A: Given problem is :

Q: Give an example of a set of numbers that is: a.Closed under both addition and multiplication.…

A: (a) Set X is closed under addition if any two elements x, y in X such that x + y in X  Set X is…

Q: 5. (a) How many functions are there from a set with n elements to a set with m elements?

A:

Q: Give an example of a relation over the set {0, 1, 2, 3} that is not reflexive, not symmetric, and…

A: We need to give an example of a relation over the set {0, 1, 2, 3} that is not reflexive, not…

Q: Using the definition of an open set, prove that the interval (0, 1) is an open set.

A:

Q: Let R C R+ x R+ with R = {(x, y)|[x] = [y]}, that is, x and y round up to the sane number.…

A: Given, R⊆ℝ+×ℝ+ with               R= x, y | x=y

Q: Let A andB be two sets of. integers. A distance measure 'd is defined as d(A - B) = size(A - B),…

A:

Q: 2| and determine for the sets, Represent the sets in the comples plane F- whether they are open,…

A: Taking z=x+iy, z-2≤z forms the following region in the complex plane.

Q: set of integers is denoted by Z

A: There is some standard notation for certain types of sets . Set of real numbers is denoted by R,…

Q: What is the possible number of reflexive relations on a set of 5 elements?

A: Introduction : We have give a set of 5 elements , we have asked for the number of reflexive…

Q: Define the real numbers R to be the set of all cuts in Q.

A: