3. List all distinct functions from the set A = {1,2} to the set B = {a,b}. How many such distinct functions exist?

Q: 9.J. If F is a non-empty closed set in R and if x ¢ F, is there a unique point of F that is nearest…

A: As per BARTLEBY GUIDELINES, I answered one question (Q-9.J.) and repost other questions separately.…

Q: Let A and B be two sets with |A| = n and |B|| = m, where n and m are positive integers. Answer each…

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Q: Suppose h is a function such that h(3) = - 2, h'(3) = 2, h'"(3) = 3, h(5) = 5, h'(5) = 7, h''(5) =…

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Q: Let A and B be two sets with |A|| = n and |B|| m, where n and m are positive integers. Answer each…

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Q: Given that f(x) contains the discrete points of {(0, 3), (1, 4), (2, 0), (3, 1), (4, 2)}, the value…

A: It is given that, function f(x) contains the discrete points of 0,3,1,4,2,0,3,1,4,2. We have to find…

Q: Given the function f:{1,2,3} → N defined by f = {(1,3), (2,5), (3,1)} Is f1-1 Is f onto What is the…

A: We know that one to one functions are functions that return a unique range for each element in their…

Q: For a function f: A --> B and subsets C and D of A and E and F of B, prove the following: f-1(E -…

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Q: Determine the global extreme values of the function on the given set without using calculus f(x, y)…

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Q: Compute the following values for the given function. uevw + veuw + weuv VW g(u, v, w) u2 + v2 + w?…

A: See attached file for a step by step explanation.

Q: Suppose f  is an odd function and is differentiable everywhere.Prove that for every positive number…

A: Since the function is differentiable everywhere, so the function is continuous too everywhere By…

Q: Let F be the collection of all functions f: N-→ {0,1}. Is F countable ?

A: A set S  is countable if there exists a one-to-one map from the set to the set of all-natural…

Q: function is defined as c*x^1 from 1 to 5 and 0 otherwise. What is c?

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Q: 4. Let A and B be sets and let T C B. Also let f : A → B. (a) Use a diagram to show that f(f-'(T)) C…

A: According to the given information,

Q: Determine which of the points in the following list lie in the domain of the function f(x, y) =…

A: Let's find.

Q: If for each element y in Set B there exists an element x in Set A such that f(x) = y, then the…

A: A function f : A → B is said to be (a) one to one function - If the images of distinct elements of…

Q: Let X and Y denote the sets containing 2 and 20 distinct objects respectively and F denote the set…

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Q: 6. Consider these functions from the set of students in a discrete mathematics class. Under what…

A: (a) The students from the set of student if it is assigned to his/ her mobile number is one to one…

Q: Consider the functions f and g, defined on R. Use set notation to represent the domain of h(x) :…

A: The given problem is related to function and its domain. We need to understand the concept of…

Q: A on S is a function from S×S into S.

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Q: A(n)________ is a function whose domain is the set ofpositive integers.

A: We know that, a sequence is a function where the domain is the set of all positive integers and the…

Q: Prove directly from the definition that if X and Y are independent and f and g are measurable…

A: Solution: Given X and Y are independent and f and g are measurable function then we have to prove…

Q: For a function f: A --> B and subsets C and D of A and E and F of B, prove the following: f(C) -…

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Q: Complete the following table of values of a function p : {3,4,..., 11, 12} {-4, -3, ...,4,5} 3 5 10…

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Q: Suppose that f : A → B and g : B → C are both injective functions, prove that the function go f : A…

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Q: Let X = {1,2,3,4} and Y = {5,6,7}. State whether a function f: X → Y can be one-to-one or not…

A: By using definition of one-time and onto function we solve the given problem :

Q: d) Let XCR be a set and f: X→ X be a function. If X is compact and convex, then f admits a fixed…

A: d) If X is compact subset of R then X is closed and bounded. If X  is convex subset of R then X is…

Q: Is the function f(x) = x + 1 from the set of integers to the set of integers onto?

A: For onto from set A to B, Every value of set B should exist atleast once in the function.

Q: Suppose, we want to define functions from set Ato set B Given that, B = n = 20 > 15 = m =HAw many…

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Q: Determine whether  the following statement is true or false, and explain why. A critical number c is…

A: Solution:GivenA critical number c is a number in the domain of a function ƒ for which ƒ′(c) = 0 or…

Q: Let, X, Y, Z be sets of sizes x, y and z respectively. Let W = Xx Y and E be the set of all subsets…

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Q: Determine whether each of the following statements is true or false, and explain why. A critical…

A: Given statement is "A critical number c is a number in the domain of a function ƒ for which ƒ′(c) =…

Q: Suppose h is a function such that h(2) = -2, h'(2) = 2, h"(2) = 4, h(5) = 5, h'(5) = 7, h"(5) = 12,…

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Q: 4. a) Determine if the credit card number 4147180124197779 has a correct check digit. Is this a…

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Q: Suppose that A and B are sets and f : A –→ B is a function. Fix subsets X,Y C A. Prove that Imf(X) –…

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Q: Differentiate the following function. y = In x+ In 5

A: The function is y = ln x + ln 5

Q: Consider these functions from the set of teachers in a school. Under what conditions is the function…

A: That is, no two elements in the domain of the function are mapped to same element of the co-domain.…

Q: Show That any constant function Set is measurable. an ameasurabl

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Q: Q1. (a) How many functions are there from a set with 3 elements to a set with 5 elements?

A: We find total number of functions from a set with 3 elements to a set with 5 elements.

Q: Let X = {1,2,3,4} and Y = {5,6,7}. State whether a function f : X → Y can be one-to-one or not…

A: By using definition of one-time and onto function we solve the given problem :

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: Given X={20,40,0,80,120,130, 140, 410,5003, Y={0,1,23,4,5,6,7,10,11}, and function f. X-Y, Vx+10…

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Q: Consider these functions from the set of students in a discrete mathematics class. Under what…

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Q: Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval…

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Q: consider the sets A=(1,2,3}, B={a,b,c} and a function f:A-B defined as f(1)=a,f(2)=c, f(3)=b. What…

A: A={1,2,3} and B={a,b,c}

Q: Show that a one-one function                 f : {1, 2, 3} → {1, 2, 3} must be onto.

A: Given, the function f : {1, 2, 3} → {1, 2, 3} is one-one.

Q: The set of all permissible inputs for a function is called the ________, and the set ofall…

A: Fill in the blanks. The set of all permissible inputs for a function is called the ________, and the…

Q: What is an injective function from a set A into a set B?

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Q: Let f and g be the function from the set of integers to itself, defined by f(x) = 2x + 1 and g(x) =…

A: Consider the two given functions. fx=2x+1 gx=3x+4   The composition of the functions f and g  is…

Q: Suppose that the functions u and w are defined as follows. u (x) =x²+4 w (6) - /x+5 Find the…

A: givenu(x)=x2+4w(x)=x+5therefore(u+w)(x)=x2+4+x+5(u-w)(x)=x2+4-x+5

Q: The following functions all have domain {1,2,3,4,5}{1,2,3,4,5} and codomain {1,2,3}.{1,2 For each,…

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