Let A and B are nonempty sets, and functionƒ maps A to B. Which of the sets below is the rang of the function f?

Q: 2. Let X be a set, and let A C X. Define a function f: P(X)→ P(X) by f(B) = AUB for all BE P(X).…

A: Given: 2) Here the given is im(f) = f(A)  A ∈ P(X) = C∈P(X)  A ⊆C, We have to show that im(f) =…

Q: For two sets A = {a, b, c}, B = {7,12, 13, 17, 30} fis a injective function from Ato B If f (a) =…

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Q: Let f: A→B be a function. Prove or disprove the equivalence: (a) f is injective (b) If C is any set…

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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: Give a proof of the following statement. Suppose A, B and C are sets, f is an injective function…

A: We have to prove the given statement.

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: Let f : A → B be a function. Show that the set P = {f ^b | b ∈ B} is a partition of A.

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Q: Assume that p is a function that is defined for x > 0 and satisfies p(a/b) = p(b) - p(a). Prove…

A: pab=p(b)-p(a)f(x)=p2-x2+x

Q: Let f : A → B be a function, {B;}jej a family of subsets of B. Prove that f-'(Njej B;) = Njej…

A: Given that f : A → B is a function. Also given that Bjj∈J is a family of subsets of B . We have to…

Q: Suppose that f : A → B is a function, C C B and D C B. Prove that Š (C – D) = } (C) - } (D).

A: Solution :-

Q: 3. Use a sign chart for f" to determine the intervals on which each function f is concave up or…

A: As per our guidelines we are supposed to answer only first three subparts of a question. Kindly…

Q: Use the graph of f to find (a) the largest open interval on which f is increasing and (b) the…

A: Consider the provided equation, y=x22x-1 Use the graph of f to find (a) the largest open interval on…

Q: Let f, and f2 be two functions from R to R such that f, (x) = x4 and f2 (x) = x - 5. What are the…

A: Given data f1 and f2 are two functions from R to R  and  f1 = x4 , f2 = x - 5

Q: If f(a) > f(x) in an open interval containing a, x + a, then the function value f(a) is a relative .…

A: Given: If f(a)>f(x) in an open interval containing a, x≠a, then the function value f(a) is a…

Q: Prove the following statements a. Let X and Y be nonempty sets and f: X→Y. If A⊆X and B⊆Y, then…

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Q: Let f: CD be a function, with C being the domain and D being the codomain. Show that for any C₁, C2…

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Q: Show that if f and g are functions on a finite set A and both one-to-one, then the composite…

A: Since you have submitted multiple questions, according to Bartleby policy we'll solve the first one.…

Q: Let g : B → C and h : B → C be functions. Suppose that go f = hof for every function f: A → B. Prove…

A: We have to prove that g(x) = h(x) for all x belongs to B.

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: For the given subsets A and B of Z, let f(x) = 2x and determine whether f: A ---------- B is onto…

A: Given :  f(x)=2xTo identify the given…

Q: A point p is recurrent for f if, for any open interval J

A: Given, A point p is recurrent for f if for any open interval J about p, there exists n>0, such…

Q: List the open interval(s) on which f

A: Given, the graph of the function is

Q: Give an example of a function f : (X1, d1) → (X2, d2) that sends compact sets to compact sets, but…

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Q: Give a proof of the following statement. Suppose A, B and C are sets, f is a surjective function…

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Q: Show that the following two statements are equivalent: i) the function f : A → B is surjective ii)…

A: i) In the f:A→B is surjective means every element in the co-domain has its pre-image in the…

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: Show that the following two statements are equivalent: i) the function f : B → C is injective ii)…

A: Given: (i)   the function f : B → C is injective (ii)     for every set A and for any functions g :…

Q: Give an example of(a) a function f : Z → N that is both one-to-one and onto N; and(b) a function f :…

A: Here, we need to give an example of(a) a function f: Z → N that is both one-to-one and onto N.

Q: Let A, B, and C be three sets, and let f : A → B and g : B → C be two functions. Assume that the…

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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: a. Prove that for any sets A,B⊆X and for any function f:X⟶Y, f(A∩B)⊆f(A)∩f(B).       b. Prove that…

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Q: Given functions f and g from a set X to a set Y, f = g if, and only if, _____.*

A: Given  functions f and g and f=g

Q: Given a function f: A → B. Define the relation f from P(A) to P(B) by f = {(X, Y ) is an element of…

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Q: Let f be the subset of Z × Z defined by  f = {(ab, a + b) : a, b ∈ Z}. Is f a function from Z to Z?…

A: Let f be the subset of Z × Z defined by  f = {(ab, a + b) : a, b ∈ Z}. We observe that  That is the…

Q: Let A and B be subsets of a set X. Prove that the functions f(x) = XAUB(x) and g(x) = XA(x) + XB(x)…

A: According to the given information, Let X be any set and A and B be any subsets of X. It is required…

Q: Given a function f : A → B. Define the relation f from P(A) to P(B) by f = {(X,Y) C P(A) × P(B)|Y =…

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Q: A number-theoretic function f is said to be multiplicative if f(m,n) = f(m)f(n): :Select one O For…

A: Introduction: When the domain of a function is the set of positive integers or more precisely the…

Q: Let f : S → T be a function, and let A and B be subsets of T. Prove or give a counterexample to the…

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Q: Let f be a function from the set A to B. Let S and T be subsets of A. Show that f(S intersection T)…

A: Given: f:A→B be a function from set A to B. and S⊆A, T⊆A We have to prove : f(S∩T)⊆f(S)∩f(T) Proof:…

Q: 7. Let A and B be sets, and let f: A → B and g: B → A be functions. Suppose that: • go f(a) = a for…

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Q: Determine all functions f from the set of posit that, for all positive integers a and b, there…

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Q: Let A and B be nonempty sets. Prove the following statements. (a) For any function f:A→A, if f◦f is…

A: (a) Let z be an element of A. Since fof is onto there is an element x in A such that fof(x)=z.…

Q: Let F be a "function" defined on the class

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Q: Let the functionf be defined as f (x) = 3 (a) Find the intervals on which f is increasing or…

A: Given function is: f(x)=x33-x22 Then this can be solved as follows:

Q: Let f be a function on an interval I and let ₁ and 2 be any two points in I. Then if f (x₁) > f (x₂)…

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Q: b. Determine whether each of these functions from {a, b, c, d} to itself is one-to-one. i. f(a) = b,…

A: We are entitled to solve only one question at a time so, I am providing you the answer of first…

Q: Let g : R → R be the function g(t) = t, and let B = [-3, 1] U [2, 3]. Express the set g(B) as an…

A: First observe the behavior of the given function  g(t)=t2 : Domain of the function is ℝ and range…

Q: Consider the rule f which maps elements in the set A into the set B and which is illustrated below.…

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Q: -For a function f, the set of all possible inputs is called the of f, and the set of all possible…

A: We need to provide the name for  Set of all possible inputs Set of all possible outputs