Select the following statements that are true.ΟΣ, .j=C(n+1,2)2161-21[13]4=1 + 1 + 1 +The function f(x) = 1³-2 2+ = 2.2™= [³/7] isis an one-to-one correspondence from Z to Z.Olff: A→ Bis a function from a set A of cardinality 26 to a set B ofcardinality 25, then f is not one-to-one.

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Answered: =C(n+1,2) °2161-41 [13] = ... 01+++ The…

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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[6-R] [CLO 23] Complete the statement of the following defintion:Definition (Intermediate Value Property). A function f is saidto have the intermediate value property on an interval [a, b] iffor every M between f (a) and f (b), there exists some c ∈ (a, b)such that
Consider the functions f : A → B, g : B → A and h : B → A such that if gf =14 and fh = 1B. Prove f is a 1-1 correspondence A - B. fla = f and 18f = f. (a) (b)
Determine if these functions are reflexive, symmetric, antisymmetric, and/or transitive. a. {(x, y) | x = ëyû} on the set of real numbersb. {(m, n) | m2 = n2 } on the set of integersc. {(a, b) | classroom a has a larger capacity than classroom b} on the set of classroomsd. {(1, 1), (2, 2), (1, 2), (2, 3), (3, 2), (3, 3)} on the set {1, 2, 3}
Determine whether each of these functions f:Z->Z is one-to-one, on-to, one-to-one correspondence, respectively. a) f(n) = n-1 b) fln)= n² +1 c) f(n)= n² d) fir) = [n/2]
1. Let A = {1,2,3}, B = B = {4,5,6}, The functions f : A → C and g: B → C are defined by f(1) = 7, f(2)= 9, f(3) = 7, Does there exist a function h: A → B such that go h = f? Does there exist a function k : B → A such that fo k = g? Justify your answers. {4,5,6}, C = {7, 8, 9, 10}. g(4) = 10, g(5) = 7, g(6) = 9.
7. Let A = {a,b,c,d}, B = {c, d, e}, and C = {f, g, h, i}. (a) How many functions are there from A to B? (b) How many one-to-one functions are there from A to B? (c) How many functions are there from A to C (d) How many one-to-one functions are there from A to C?
13. (9 points) Let D be the set of finite subsets of positive integers. Let S be the set of all positive integers greate than or equal to 2. Define a function T:S → D as follows: For each integer n ≥ 2, T(n) = the set of all even factors of n. a) Find T(10). b) Find T(17) c) Find T(m), where m is any odd positive integer.
{1,5,10,15} and Y1 = {1,5,10,15,20}. Using the formal definition of a function, determine which of the following subsets of X1 × Y 1 correspond to the functions of X1 → Y 1. Justify your Problem 7. Let X1 = answer by providing reasons why each is or is not a function. 7(a) f = {(1,15),(5,10),(1,5),(10,1),(15,1)} 7(b) f = {(1,20),(5,1),(10,1),(15,5),(1,20)} 7(c) f = {(1,1),(5,1),(10,1)}

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=C(n+1,2) °2161-41 [13] = ... 01+++ The function f(x) = [37] is an one-to-one correspondence from Z to Z. Olff: A → B is a function from a set A of cardinality 26 to a set B of cardinality 25, then f is not one-to-one. -1 21 +2 = 2-2