Let D be the set of all finite subsets of positive integers. Define a function T: Z+→ D as follows: For each positive integer n, T (n) = the set of positive divisors of n. Find the following: a. T(1) d. T (5) b. T (15) e. T (18) c. T (17) f. T (21)

Q: Suppose f: R → R is the squaring function, that is, f(x) = x² for every real number . Mark all of…

A:

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

A:

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: Consider the following function: f: Z → N given by f(x) = (x+4)² + 8; where, as usual, Z and N,…

A:

Q: Let f: R →R be defined as Sr + 2, if a < 1, 1-2a, if a 21. S(1) Plot f(r) of f of all r) Based on…

A:

Q: consider set a and b with |A| = 9 and |A| = 20 a. how many functions f : A -> B are there b. how…

A: Given set A and set B with A=9 and B=20 (a) We have to find the number of functions f:A→B. The…

Q: b) Let the set A = {-1,0, 1} and consider the following function: f2 A → A given by f₂(x) = (-x)4.…

A:

Q: 2. Let X1 and X2 be sets. Define functions T1 : X1 × X2 → X1, T2 : X1 × X2 → X2 by T| (X1, X2) = x1,…

A:

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: Consider the set of all functions f : N → {0, 1}, i.e., the functions map the natural numbers to 0…

A:

Q: 2. Let R be the relation on the set A = (1, 2, 3, 4, 5, 6, 7} defined by the rule (a,b) e R if the…

A:

Q: Let A, B and C be sets, and let g: A->B and f:B‐>C be functions. Prove if f, g are surjective, then…

A: The solution is given as

Q: Let R = {(n, −n) | n ∈ Z and n ≤ 0} ∪ {(n, n + 1) | n ∈ N}. Is R a function? Justify your answer.

A:

Q: the following definition using symbols:  A function f(x) is increasing iff for every real x and…

A:

Q: Prove or provide a counterexample to the following statement: if f : A → B and g : B → C are…

A:

Q: let a= {0,4,9,1.6} , b={0,3,6,12,20} and f a function. from a to b with f(x)=√x + x. A. Find f(0),…

A:

Q: Let f(x) = x and g(x) = x-8. Determine the composite functionfog and its domain. %3D (fo g)(x) =…

A: given that fx=x and gx=x3-8determine the composite function fog and its domain

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: (a) Give an example of two functions f: A→B and g: B-C such that f is both 1-1 and onto but gof is…

A: (a)let's define sets 𝐴, 𝐵, and 𝐶 as follows:Let 𝐴={1,2}Let 𝐵={3,4}Let 𝐶={5}Now, let's define…

Q: Let f be an arithmetical function which is not identically zero. If f is multiplicative, then f(1) =…

A:

Q: Let f be a function defined on an interval I. All we know about f is that there is a constant K> 0…

A: Concept:

Q: Let f: R+ → N+ with f(x) = [x²]; that is, f(x) returns the square of x rounded up. Characterize f in…

A:

Q: Let A, B and C be sets, and let g: A → B and f: B → C be functions. Prove: (i) If f, g are…

A: (i) Let, f : B → C and g: A → B are injective.      Now, f ◦ g is a function from A to C.…

Q: Let A = {2, 3, 4, 5} and B = {6, 8, 10}. A relation R is defined from A to B by a R b if a | b and…

A:

Q: Suppose f: R→ R and g: R → R are functions, and the composite function fog is a bijection. Which of…

A: introduction If a product f: A B meets for both invertible (yet another product) and done by…

Q: Let f = (1, 6) (2, 3, 5, 4). Compute each of the following powers of f.   f-2

A: We have given the permutation :  f=(1,6)(2,3,5,4) We have to compute : f-2

Q: Let S be the set of all strings of a's and b's of length 3. Let B = {0, 1}. Let f: S B be defined as…

A: S be the set of all strings of a's and b's of length 3 . Then to find f(aaa) , f(aab) , list all the…

Q: Let f : A → B and g : B C be surjective functions. Prove or disprove whether gof is surjective.

A: Here given that                       f :A→B   and    g :B→C  be both surjective function .  Now we…

Q: The domain of a composite function (f o g)(x) is the set of those inputs x in the domain of g for…

A: We have tell the domain of a composite function (f o g)(x) is the set of those inputs x in the…

Q: Consider the function f(x) = e* – 1, the third approximation of the zero p3 of f using Nweton's…

A:

Q: Given f: R → R where f(x) = x³ Is it a function or not? If function, identify whether it is…

A:

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: . For nonempty sets A, B and C, let f : A → B and g: B → C be functions. (a) Prove: If g of is…

A:

Q: f(x)=x² +3

A:

Q: Let f A → B be a function that is one-to-one and onto, and let C be any set such that CCA and f: C →…

A:

Q: Find sets A and B, subsets C and C2 of A, and a function f : A → B so that AC: N C2) c ACi)NAC2). 6.

A: Let A = B = R (set of all real numbers) and let C1 = [-2, 0] and C2 = [0, 2] be subsets of A = R

Q: Prove the following statements: (a) If f : A → B and g : B → C are one-to-one functions, then go f:…

A: We prove that if f : A → B and g : B → C are one-to-one functions, then go f : A → C is one-to-one.…