(a) How many functions are there from {1,2,3,4,5} to {A, B, C}? (b) How many onto functions are there from {1,2,3,4} to {A, B, C}? (c) How many bijective functions are there from {1,2,3} to {A, B, C, D, E}?

Q: 6. Show that if f : X Y and g : Y → Z are both onto then fg : Z -→ Z is onto. (Note this is function…

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Q: 4. Let F : A --> B, g : B --> C, and h : B --> C be functions, and suppose that f is onto. Prove or…

A: Given: f:A→B, g:B→C and h:B→C are the functions and f is onto.

Q: Using Richard Hammack's book of Elements of Discrete Mathematics chapter 18 in cardinality.…

A: We need to show that there exists a bijective function φ : (0, 1) → (0, ∞). Here first, we will…

Q: Suppose that f is a function from A to B, where A and B are finite sets with |A| = |B|. Show that f…

A: Given that f is a function from A to B, where A and B are finite sets with A=B. We have to show that…

Q: Let A = {0, 1, 2, 3, 4, 5}, B = {1, 3, 5, 7, 9}, and C = {0, 2, 4, 6, 8} k. Is {0} ⊆C? l. Find the…

A: K. Yes {0} is a subset of C.  I. Card (C) = 5 Hence card ( P(C)) = 25…

Q: Q1 Show that by using Laws that if the compound statement is logically equal. [p ⋀ (~ (~p⋁q))] ⋁…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

Q: 6. If f is bounded above function on [a, b] and let P be a partition of [a, b), then A. L(f, P)…

A: Given :

Q: 5. (a) Suppose f: N→ Z is a one-to-one onto function. Prove that the function g: N × N → N x Z…

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Q: (a) In how many ways can 20 people be arranged in a circle if rotations are considered equivalent?…

A: Answer :

Q: C. Show directly from the definition (without using Arithmetic of Limits or similar results) that…

A: Topic:- continuous function

Q: Let x={1,2,3,4} and y={1,2,3,4,5,6,7,8,9,10}   and "f" from X to Y is given by…

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Q: (a) How many one-to-one functions are there from a set with five elements to a set with six…

A: A function f is said to be one-one if ff(x)≠f(y)  if x≠y

Q: 7. Prove that if f and g are continuous then so are max(f, g) and min(ƒ, g).

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Q: A function f is defined on the set N of natural numbers by f(0) = 2, f(2) = 5 and f(n) = 2 f(n - 1)…

A: please see the next step for solution

Q: 20 - If f is a function on a set A= {1,2,3,4,5} such that f= { (1,2), (2,3), (3,4), (4,x), (5,5)}.…

A: Use the property that in bijective functions each element of doamin and codomain has image and pre…

Q: A function f that satisfies the hypotheses of Rolle's Theo- rem on [-2, 2] and for which there are…

A: Rolle's theorem states that if a function f is continuous on the closed interval [a, b] and…

Q: 6. (a) Use the Schröder-Bernstein Theorem to prove that [a, b]| = |(a,b)| for any a, b e R. (b) Use…

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Q: Let A = {1, 3, 5, 7, 9, 11}, B= {a, b, c, d, e}, and ƒ be the function from A to B defined as below:…

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Q: A = {−4,−3,−2,…,2,3,4} and we are given the equivalent relation R on A defined by: m R n ⇔5|(m2−n2).…

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Q: 3) Let X be a set with > 3 elements. Show that there exist bijective functions f :X → X and g : X +…

A: Let x=1,2,3 then, f=123132g=123321 `

Q: A function f() from {a, b, c, d} to { 1, 2, 3, 4} defined by f(a) = 3, f(b) = 2 and f(c) = 1 and…

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Q: If X = {a, b, c} , Tx = {0, X, {a},{b, c}}, Y = {x, y, z} and ty = {Ø, Y, {y}} then f = {(a, z), (b,…

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Q: Let f(n) be the number of subsets of n] in which the distance of any two elements is at least three.…

A: Let f(n) be the number  of subsets in which distance of any two elements is atleast three

Q: The domain of f(x) = /x + 1 - – /1 – x is O [-1, ∞) O (-∞, 1] O (-∞, –1] U [1, ∞) O [-1, 1] None of…

A: We need to tell the domain of the given function: f(x)=x+1-1-xFor calculating the domain, the…

Q: 6. Determine all fun et ions f analytic in |z| < 1 and satisfying k+ k2 1+k2 k = 2,3, 4, ...

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Q: 15 - Let f be the function f: A -> B. A, B and f are defined as {1, 2, 3, 4} {5, 6, 7, 8} f = {(1,…

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Q: Prove Proposition 3.4. A monotone function that is defined on an interval is measurable.

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Q: Let x be a positive integer and let R = {a1, a2, a3, . . . , ax} be a nonempty set where ai are real…

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Q: 2. Suppose I wish to define a function g : {0, 1, 2, 3, 4} → Z that takes an input of an equivalence…

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Q: Let N = {1,2, 3, 4} Suppose that G = {0, {1}, {3}, {1,3}, {2, 4}, {1, 2, 4}, {2, 3, 4}, N} is a…

A: Given: Ω=1,2,3,4 To find: a) Smallest σ field b) Decide which of X and Y are G measurable.

Q: Which functions on {1, 2, 3, 4} x {a, b, c} is NOT onto? О {1, с). (2, а). (3, b). (4, b)} О {(1,…

A: Given sets are {1,2,3,4} and {a,b,c}. We know that a function f from A to B is called onto if for…

Q: Show that the set of functions from the positive integers to the set {0, 1, 2, 3, 4, 5, 6, 7,8, 9}…

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Q: True or false a. Every permutation is a one-to-one function b. Every function is a permutation iff…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: (a) How many injective functions are there from {1, 2, 3} to {1, 2, 3, 4, 5, 6, 7}?

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: (a) Consider the customers with IDs ranging from p to q, inclusive, where p< q and consider the…

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Q: Simplify the Boolean function F together with the don't-care conditions d in (1) sum-of-products…

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Q: Let Z be the set of integers, A = {-1,0,1,2,3,4, .... }, and M = Define f(x) = x². Which among the…

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Q: o How many different functions are there from a set with 5 elements to a set with 7 elements? o How…

A: 1. How many function from a set with 5 elements to a set with 7 elements.2. How many one ot one…

Q: c) Let X- {p, q, r, s, t}, Y= (1, 23} and z={k, e} 1. Define one-to-one function and how many…

A: One to one function: Let us define a function f:A→B is said to be one to one function if…

Q: 4. Which of the following set represents functions? * O A=((2,5),(1,0),(3,1),((4,2)}…

A: We first find which of the the given set represents a function.

Q: 1. Let X be a set with n elements. Compute the number of distinct functions f: X → X. How many of…

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Q: group of order 35 acting on a set of size 16.

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Q: Let X= {p, q, r, s, t}, Y= {1, 23} and Z={k, e} Define one-to-one function and how many one-to-one…

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Q: 2. Proposition 1 Let the function H from S1 x Sz into R be 2-increasing and grounded. • Prove that H…

A: We know, A 2-place real valued function H is 2-increasing function if VHk≥0 for all Rectangles.…

Q: Simplify the Boolean function F together with the don't-care conditions d in (1) sum-of-products…

A: The complete solutions are given below

Q: = function satisfies the three hypotheses of Rolle's Theorem on the given interv. n of Rolle's…

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Q: True/False: The permutation f on A = {1, 2, 3, 4} given by f(1) = 2, f(2) = 4, f(3) = 3, f(4) = 1 is…

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Q: 8.4 Let f=(x1,x2...,x,)E S,. Show that o(f)=r.

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Q: Let f = {(1,1), (2,3), (0,–1), (–1, –3)} be a function from Z to Z defined byf(x) = ax + b, for some…

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Q: .Express the Boolean function F(A,B,C)=E(1,3,5,7) in products-of-sums form .Express the Boolean…

A: Any Boolean function can be rewrite as a sum  of its 1-minterms. The notation is given by F(list of…