1. Let the universal set be R, the set of all real numbers, and let A = R| – 12 < x < 3}, B = {x € R – 3 < x < 8}, and C = {x € R|5 < x < 12}. Find each of the following: {x € %3D 1. AUB 2. AN B 3. АС 4. AUC 5. В — С.

Q: 3.Determine the intersection X ∩ Y. Express the  in interval notation. X = {x/ x>equal 8} and Y =…

A: We have: X=x  x≥8=[8,∞)Y=x  x&lt;7=(-∞,7)

Q: Express the following, denoted in red, in interval or set notation -6-5-4-3-2-1 0 1 2 3 4 5 6 7 8 9

A: In mathematical notation, open intervals and closed intervals are denoted using brackets and…

Q: 3. Let a, b, c, d be real numbers with a < b and c < d. Find a one-to-one correspondence between (a,…

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Q: 1. example of sets A and B for which A B but Ag B.

A: Cardinality of a set is number of elements in the set.

Q: • Rewrite each of the following sets in interval notation. R: 23 23}

A: We have to rewrite each of the following given sets in interval notation :

Q: Indicate the least upper bound of the following sets. If a set does not have a least upper bound,…

A: We have to find the least upper bound of the given set.

Q: Please fill in the blank. (2 pts, 0.5pt each, due in lab) a. Si S2 = {-3, 1, 4} b. S1'| × |S2| = c.…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: 6. Suppose that inf A > inf B. a. Show that there exists a € B such that a is a lower bound of A. b.…

A: 6a) Given: Two sets A and B such that infA&gt;infB, To Prove: there exists an element a∈B which is a…

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

A: We will just use of definitions of different type of sets

Q: 11. If |A| = 3, how many relations are there on A?

A: Given A=3

Q: 6. Let X and Y be subsets of {a,b}. Write the relation where X is related to Y if |X| = |Y| as a set…

A: Let  A={a ,b }  Cardinality of A=2 so the cardinality of power set is 2^2 =4 Now power set of A is…

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

A: Solution

Q: Find the complement of the set given that  U = {x | x  I and −3 ≤ x ≤ 5}.  (Enter your answers as a…

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Q: Find the indicated sets. (a) P({1,2} × {3}). (b) P({1,2}) × P({3}). (c) {X e P({1,2,3}) : 2 EX}.

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Q: 3. True or False. Determine whether the given pairs of sets are equal. a. A = {2n + 1|n E W} ; B =…

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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: Prove that if x is a real number such that x ≥ 0 and x ≤ € for all € E R where € > 0, then x = = 0.

A: This question is from real analysis.Answer given below.

Q: Let N={1,2,3,4,...}. Let P(x,y) be the predicate that x is less than or equal to y^2

A: (d) S = {1, 2, 3, 4, 5, 6, 7, 8, 9} (e) T = {3,4,5,6,......} (f) R = {} (empty set)Explanation:(d)…

Q: Let A = (x = R: 7 ≤x < 20} and B = {7, 18, 19, 20, 21). What is A - B? A. {x ER: (7<x< 18) (18 < x…

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Q: Find the following cardinalities: a. A = {5, 10, 15, ..., 75} |A| = b. A = {x € Z: - 100 ≤ x ≤ - 17}…

A: We have to find the cardinality of the following setsWe know thatThe cardinality of the set is the…

Q: Determine the intersection X ∩ Y. Express the in interval notation. X = {x/ x>equal 8} and Y =…

A:

Q: 1. List the elements of each of the following sets by using the roster method. (a) the set of all…

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Q: 2.4. Let A and B be sets of real numbers, let f be a function from R to R, and let P be the set of…

A: As per the policy, we are solving three parts. Please repost it and specify which part is to be…

Q: A = {y EZ:2 < y ≤ 9 and y is odd}. B = {1, 4, 6} C = {yEZ: y ≤ 10 and y is even}. D = {y EZ: y ≤ 7…

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Q: For each of the following sets, tell if it an infinite set, finite set or an empty set. v 1. {x E R:…

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Q: C and D are sets of real numbers defined as fo C={x |x< 4} D= {x |xs7} Write Cn D and CUD using…

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Q: Find the cardinality of each of the following sets. a. A = {x:xe Z and x² = -9} b. B = {x:x € R and…

A: The given sets,(a) (b) (c) (d) The aim is to find the cardinality of each of the given sets.