2. Show that the following two sets have the same cardinality, by proving |X| ≤ Y andY|≤|X:X = R, Y = (0, ∞) U (-3,-2).

Answered: Image /qna-images/answer/69573d4d-e88b-4ecf-a0ce-ed3b7a991787.jpg

Answered: 2. Show that the following i two sets…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let the universal set be R, the set of all real numbers, and let A = {x € R| – 4 < x < 1}, B = {x E R|–1 < x < 3}, C = {1,2,3, 4} Find each of the following. а. А uв b. A пВ с. Вс d. A пС 5.
I provided an example. Please solve the problem accordingly
Consider following five sets: I. { , } { } II. { } III. IV. { , , } V. { , } Find all linearly independent set(s). (a) I (b) I and IV (c) I and II (d) II, IV and V (e) II (f) II
Show that for every pair of sets X and Y, the sets X × Y and U {(x, y) | y ≤ Y} xEX are equal.
Q: State whether the following statements are true or false: 1. Let S be a non-empty subset of the set of real numbers R. Ir s is bounded above, then Sups is exist, but need not to be unique in general. 2. If A = (-5,5) and B = (5,10), then Inf(A + B) = 10 and Sup(A + B) = 15. 3. The closed interval [1,2] has no maximal element. 4. The set of natural numbers N of R is unbounded. 5. The set of real numbers R, has Sup(R) = o and Inf(R) = -co. 6 The set S= (x E RỊ x? - 25 s 0} has Max(S) = 5 and Inf(S) = -5 with no minimal %3D element. 7. The set S = {1+nez*} has Max(S) = 2 and Min(S) = 1. 8. Every bounded set of real numbers R has maximal and minimal elements. 9. The properties (M2) and (M2) of the definition of the metric space are state that the distance from any point to another is never negative, and that the distance from a point to itself is zero. 10. There are many metric functions d: M x M -R that can be defined on a non-empty set M.
each part below, indicate (by making suitable arguments) whether the following sets are open (yes/no), closed yes/no), and bounded (yes/no). Hint: You should probably graph the following sets. The straight line connecting the points (a, b) and (c,d) (including the endpoints) in R² where a < b
Prove: bd (s) = 5 TR-S bd (s) is a closed set
Let Vi = x ℝ − 1 i ≤ x ≤ 1 i = − 1 i , 1 i for each positive integer i. Find each of the following. (Enter your answers using interval notation.) (a) ∪4i = 1Vi = (b) ∩4i = 1Vi = (c) Are V1, V2, V3, mutually disjoint? Explain. a.) Yes, because the intersection of the sets V1, V2, V3, ... is empty. b.) Yes, because no two of the sets V1, V2, V3, ... have any elements in common. c.) Yes, because the union of the sets V1, V2, V3, ... is empty. d.) No, because no two of the sets V1, V2, V3, ... are disjoint. e.) No, because the sets V1, V2, V3, ... are disjoint. (d) ∪ni = 1Vi = (e) ∩ni = 1Vi = (f) ∪∞i = 1Vi = (g) ∩∞i = 1Vi =
Only Need Part(d), thank you!

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2. Show that the following i two sets have the same |Y|≤|X: cardinality, by proving X ≤ Y and X = R, Y = (0, ∞) U (-3,-2).