Given: f = {(a,b),(b,a),(c,b)} a function from X = (a,b,c) to X a). Write f ∘ f as a set of ordered parts.  b). Write f ∘ f ∘ f as a set of ordered pairs.  Define : f^n = f ∘ f ∘...∘ f to be the n-fold composition of f with itself. Write c). f ^9

Q: Let A, B, C denote sets. Let g, h : A → B and f : B → C denote functions. Assume f is one-to-one and…

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Q: Prove or disprove: composition of functions is commutative; that is g◦f = f ◦ g when both sides are…

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Q: Find an example of a function f: R → R which is (a) surjective but not injective (b) neither…

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Q: Let A = {1, 3, 5, 6, 7, 9, 10, 12} and B = {1, 2, 3, 5, 7, 8, 9, 11, 12}. Consider the following…

A: Given a function f: A -> B , we have to determine whether it is injection, surjection,…

Q: What kind of functions is the function shown in this figure? b) odd e) Neither odd nor even d) None…

A: Consider the provided graph, A function f(x) is even if the graph of f(x) is symmetric with respect…

Q: Let f, g be two functions from a set A to itself. If f o g is surjective, does it imply that g o f…

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Q: Let A = {1, 2, 3, 4} and let f:A ->A be defined as {(1, 3), (2, 4), (3, 1), (4, 3)}. Is f…

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Q: Let A = {a, b, c}. Define the function f: p(A)→N, by f(X) = card(X), where p(A) be the power set of…

A: Given A = {1,2,3} then ρ(A) = {ϕ , {a} , {b} , {c} , {a,b} , {a,c} , {b,c} , {a,b,c}} Define f :…

Q: Let A = {1, 2, 3, 4, 6}. Let R be therelation on A defined by {(a, b): a , b ∈A, b is exactly…

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Q: Let A = B = {a, b, c, d}. The function f is defined from A to B which is given below: f = {(a, a),…

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Q: True or false: There exists a monotonic function f: R → R whose range is the set of integers. True…

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Q: Let f : A →B and g : B →C denote functions, and assume g ◦f is injective. a. Prove or disprove: The…

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Q: Let A = {a, b, c, d} and f = { (a, 0), (c, 12), (d, 18), (b, 12) }. Is f a function from A to B ?…

A: Given, A = {a,b,c,d} f = {(a,0) , (c,12) , (d,18) , (b,12)}

Q: Let f: A -> B and g: B -> C be two functions. Prove: if f and g are surjective, then gof is…

A: Given: Let  f: A→B and g: B→C be two functions.  If f and g are Surjective(onto), To Prove:  g∘f:…

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: 3. Let A = {1, 2, 3, 4}. Let F be the set of all functions from A to A. (a) How many pairs (f, g) E…

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Q: THEOREM Let f be a function from A into B. If A, and A2 are subsets of A, then (b) f(A, N A2) C f(A)…

A: We solve this by drawing related picture.

Q: Let A = {d, e, f} and B = {0, 1} Define a relation as follows: ARB = {(d, 1), (f,0)} Select the…

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Q: Let A = { -1, 0, l}. Find mappings f: A -------------- A and g: A --------- A such that f o g ≠ g o…

A: Here given  A=-1, 0, 1 Now consider two functions as f:A→Afx=1g:A→Agx=0

Q: Use two of the following sets for each part below. Let X = {a,b,c}, Y = {1, 2, 3, 4} and Z = {s, t,…

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Q: Let f: A → B be a function, and let C be any set such that BCC. True or False: f : A → C is always a…

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Q: Consider the function G below: G Select all statements below that are true: Rng(G) = (a, b, c, d, e)…

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Q: Define the relation A,= [(x,x + 1): x E R] Show that A, is a function from R to R.

A: Given relation △x=x, x+1: x∈R is defined on Real number set R. Now a relation is said to be function…

Q: 3. Let A = {1,2, 3, 4}. Let F be the set of all functions from A to A. (a) How many pairs (f, 9) €Fx…

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Q: Let A- (Blanche, Rose, Sophia, Dorothy), B-(Red, Blue, Yellow) and consider the function f: A B…

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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 R = {(a, b), (a, c), (c, d), (a, a), (b, a)}. What is R ° R, the composition of R with itself?…

A: R = {(a, b), (a, c), (c, d), (a, a), (b, a)} R°R = R2 = { (a, a), (a, d), (a, b), (b, b), (b, c),…