1] Find the supremums of the following sets by proving your results: a) S = {a < x < b; x E R}. b) S2 = {a < x < b; x E R}. c) S3 = {a < x < b; x E R}. d) S4 = {a < x < b; x E R}.
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![1] Find the supremums of the following sets by proving your results:
a) S = {a < x < b; x E R}.
b) S2 = {a < x < b; x E R}.
c) S3 = {a < x < b; x E R}.
d) S4 = {a < x < b; x E R}.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4f2a9af5-1cf5-4675-b1a2-98769bde15ff%2F25ba3bd7-4a32-4a61-a267-4698194b9bd9%2Fqn0o7d_processed.jpeg&w=3840&q=75)
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- Solve for B please.-, answer the following questions: -w³ (w+2) ³ (w - 4) ³ (w - 3) Given m(w) w7 (w + 2) (w-3)³ (w +9)¹ Round all answers to 3 decimal places as needed. If the answer doesn't exist, type DNE. a) The domain of m in set notation and interval notation is: Set Notation: {w w is a real number and w Interval Notation: 0 (-∞, -9) U (-9, -2) U (-2, 0) U (0, 3) U (3, ∞0) b) The w-intercept(s) are: c) The vertical asymptotes of m are at w Write the answer(s) as just numbers separated by commas. d) m has a hole at the ordered pair: Write each hole as an ordered pair. Do not do any rounding until the final answer. e) The m(w)-intercept is: ODNE f) The end behavior of m is: RH: As w LH: As or wor → m(w) Om(w) -∞ (4,0) 8 -9,-2,0,3 Horizontal Asymptote: DNE Write the horizontal asymptote as y = # if it exists. If it doesn't exist, type DNE. OF 0, 9 (3,0), (-2, 607.247)a Are ALL the following three pairs in the relation R: (4.2) (1,2) (5,1) b Is 4 a minimum element? c Does the set S have a first element? d Does the set S have a last element? e Is the set S well ordered? May you explain the answers , discrete maths?
- 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 < bVI.[15] Let the Universal set be the set R, of all real numbers. [ Hint: Use real number line to represent each set then answer parts a, b and c] A = {x eR|-3(a) Suppose a, de N. Define what it means to say that d divides a. (b) Find all natural numbers d such that d | 24 but d | 30. (c) Suppose a, b, d E N and that d | a and d | b. Prove that d | a² + b. (d) Suppose X is a non-empty set of real numbers. Define what is meant by an upper bound for X. If X has an upper bound, define what is meant by a supremum for X. (e) Let -{n-1: EN}. {" X = Find (with proof) the supremum of X.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 =Is the following set connected: V = {(x, y) € R² | 1 < x² + y² <4}? Briefly justify your answer.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 ≤ 3Adding to more parts of same question: 7: f(i)≠f(i+1) for all i ∈ Z set , number, statement or meaningless 8:{n∈Z: f(n)∈ AUBUC} set, number, statement or meaninglessModern Algebra:a) Let A, B, U and V be any sets such that A CU and BC V. Is (A × B) C (U x V)? Justify your answer. b) Suppose f:R → Z where f(x) = [2x – 11. i. If A = {x |1 < x < 4}, find f (A). ii. If B = {3,4,5,6,7}, find f (B). iii. If C = {-9,-8}, find f¯1(C). c) Let f:R → R be defined by f (x) = 2x² + 2x – 12. Is fone-to-one? Justify - your answer.Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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