Problem 1. A set ICR is called an interval if for all triples of real numbers x, y, and z such that x < z < y, if x € I and y € I then z € I. Prove that every interval takes exactly one of the following nine forms: (-∞,b), (-∞,b], (a,b), (a,b], [a,b), [a,b], (a, ∞), [a, ∞), or (-∞, ∞).

Q: Write true otherwise false if the pairs of sets are equal,{{1}},{1,{1}}

A: Two sets A and B are equal if A and B  have the same elements.

Q: Give examples of the following, and provide justification as to why your answers are examples of the…

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Q: 2. Let B,C,D,E be the following sets: B = {x|x a real number, x² <4}, C = {x|x a real number,…

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Q: Assume that a and b are real numbers such that a <b. Prove that the interval (a,b) is an open set.…

A: Given that a and b are real numbers and a&lt;b. Prove that (a,b) is an open set

Q: Q1. (a) Let R be the universal set and A = [-7,3], B = (0,8) C = {x:x≤ 10, x € R}. Find of the…

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Q: Given the function f= {(n,n²)such thatn< 3,n€N} as a set of ordered pairs in set-builder notation,…

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Q: Define E to be the empty set and further define F = {E}, G = {F}, H = {E, F}, and I = {E, F, G,H}.…

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Q: B and C are sets of real numbers defined as follows. B={y|y≥4} C={y|y<7} Write B n C and B U C using…

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Q: Question 2. Show that the relation R in the set R of real numbers, defined as R = {(a, b) : a <b} is…

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Q: 2. Let X= [0, 10] be the universal set and A = [1,4], B = (2,8), C = [3, 6) be the subsets of X.…

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Q: 4) Let a < b be real numbers. Prove that the half open/half closed interval (a, b) is both an Fo and…

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Q: Let M = R and set Question 2 4= [(-1,5) N*]U ((8,9] (7,10]), B = {æ € R: \r-4|< A= 5x 15-51215} - 4…

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Q: Which of the following pairs of sets can be placed in a one-to-one correspondence? Why? (a) { a, b,…

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Q: 2. Let A = [1,3], B = {5}, and C = [4,6]. Write the inequalities (or equalities) that specify each…

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Q: [16] 1. Represent each pair of sets A and B on a number line, then find AUB and An B in interval…

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Q: Suppose that the universal set for all variables is Z, and let P(a, b, c) be the predicate a^2 = |b…

A: Given: The universal set for all variables is ℤ. Pa, b, c is a predicate a2=b-c. To provide:  (a) an…

Q: In this group of problems, you are given two statements, A and B: determine whether one statement…

A: Solution

Q: Let A = {1,2,3,4,5,6}, how many different relations are there on a set A?

A: First, we need to know definition  of the Cartesian Product of a set is with itself. The Cartesian…

Q: F and H are sets of real numbers defined as follows. F={y|y21} H= {y |y>7} Write FUH and FnHusing…

A: A set is a well-defined collection of objects. The objects, which belong to the set, are called…

Q: Given three sets A, B, and C. A = {x €Z|-2<x<1},B= {x€Z]x2-1=0}, C= {0, – 1,- 2, -3}. (a) List…

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Q: Define the following sets: A=(1,3,7,9,10) 6-(2.5.7.8.9.10) C = (0,1.3.10) D=(2,4,6,8,10) E=xxis a…

A: Natural numbers do not include negative numbers.

Q: Let R be the set of real numbers, C= (0, 10], D= (9, 15], E = {1, 2, 3} and F= (7, 10). Find: (i)…

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Q: (b) Determine whether the following statements below is true or false. universal set = {0,1,2}…

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Q: (10) Prove that P(A)n P(B) is equal to P(An B) for any sets A and B. What can we say if the…

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Q: (iv) Prove that for any sets A, B,C we have A U (B nc) = (AU B) n (AUC)

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Q: 1. Two sets A and B as under: A = {(a, b) e Rx R:a-5 < 1 and b-5< 1}; B = {(a, b) e Rx R: 4(a-6) +…

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Q: -w³ (w+2)³(w - 4)º(w - 3) w² (w + 2)³ (w − 3)³ (w+9)¹ Given m(w) Round all answers to 3 decimal…

A: According to the Bartleby Guidelines, we can answer only first three subparts of a question at a…

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

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Q: (i) If A and B are two sets such that ACB, then m* (A) ≤m* (B).

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Q: 5. Let the universal set be R, the set of all real numbers, and let A = {x € R| – 4 <x< 1},B = {x €…

A: Given the universal set as ℝ, the set of all real numbers. Let A={x∈ℝ| -4≤x&lt;1}, B={x∈ℝ|…

Q: Number 3

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