let A be a set with n elements and B a set with m elements. How many different functions are there from A to B? Explain. If we assume n ≤ m, ho wmany one-to-one functions from A to B are there? Explain. If we assume n > m, how many one-to-one functions from A to B are there? Explain

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: Sean A, B, Cand Dinfinite sets such that TO = Cand B= D. Consider the following sets F = {f| f : A→…

A: Given that, Sean A & C and Dinfinite sets such that A=C and B= D. We have to shown that F=G We…

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: c) Let A = {x|x € S} and B = {x|x € Z;0 < x < 6}. S is set of vowel letters and Z is set of %3D…

A: Remark: A function from A to B is said to be bijection if f is both one-to-one and onto. Now f is…

Q: For what values ofn will the set {(1,3),(2,5),(n– 1,1),(n,7),(n+ 1,0) represent a function? A neR B…

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Q: ive an example of a function f. N-> N (N is the set of natural numbers) that is neither one-to-one…

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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: If F is a function and dom(F) is a set, then F is a set. Hint. Prove first that ran(F) is a set.

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Q: 8. Let the functions f: A → B, g:B → C,h: C → D be defined by the figure below. A B h D 3 a. Which…

A: Consider the functions f:A→Bg:B→Ch:C→D

Q: Let A and B be finite sets with |A| = m and |B| = n. a) How many functions are there from A to B? b)…

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Q: show that A0 subset f-1 (f(A0)) and that equality holds if f is injective

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Q: 10.3. Let A be a nonempty set. If Ris a relation from A to A that is both an equivalence relation…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 7. Identify the domain of the set (5, 3), (0,-4), (2, 5), (11, 3) and tell if the relation is a…

A: We have to identified the domain of the set  (5,3),(0,-4),(2,5),(11,3)

Q: You are given two sets, A = {a,b,c,d} and B = {1,2,3}. How many relations can be defined from set A…

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Q: 18. What can you deduce about the sets X and Y if you know, a. there is an injective function f: X…

A: Given that two sets X and Y.a)There is an injective function

Q: f : A → B is a function, X is a finite subset of Z, and k is a positive integer For each of the…

A: Given: f : A → B is a function, X is a finite subset of Z, and k is a positiveinteger. We have to…

Q: Recall the defintion of the power set of an arbitrary set, A: We say the set of all subsets of A,…

A: Given function is, So, the required diagram is,

Q: 11. Let A = {1,2,3,4} and B = {A, B, C, D, E}. Consider the following relations and state whether…

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Q: 1 Using set builder notation, what is the domain for the function g(x) 4.x2 9. A {x ER | x+ -1.5 or…

A: Set Builder Notation is a mathematical notation for describing a set by enumerating it's element or…

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: Which of the following set (or relation) represents a function: O{(4,1), (8,2), (13,2), (19,4) } O…

A: We have to determine which relation is a function.

Q: Write each of the following sets using a defining property (Ax- iom of Specification) and using a…

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Q: Consider functions ƒ : {1,2, 3, 4, 5, 6, 7, 8} → {a, b, c, d, e, ƒ}. How many functions have the…

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Q: If f A —> B and g : B —> C are injective function, then gof: A —> C is an injective function. Prove…

A: Given that f: A→B is given injective. this implies cardinality of set A is less then cardinality of…

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

A: FORMULA :-

Q: Let X = {a} and y = {a, b}, do the following. (a). Use the set-roster notation to write set (X x X)…

A: Define a relation which violate the well define ness

Q: 5. In the table, indicate if the expression is: 1) a function, 2) onto, 3) one-to-one, and 4)…

A: To find: First column of given table is: A function, onto, one-to-one and bijective.

Q: Assume that the universe is the set of all real valued functions (a) Write the following statement…

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Q: A = {1, 2, 3} and B = {a, b}. Write a function from B to A. (d) Let R be the relation not equal…

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Q: w many different functions are there from a set with 10 elements to sets with 2 elements?

A: product rule : If one event can occur in m ways and a second event can occur in n ways ,the number…

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: example of a function from R in R for which f (A) = B for all A and B open sets in R, but which is…

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Q: Consider the function that assigns each positive integer to its FIRST (leading) digit. (For example,…

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Q: 3. Let A and B be finite sets with |A| = m and |B| = n. a) How many functions are there from A to B?…

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Q: Seven players are playing 5-card stud. Each player initially receives 5 cards from a deck of 52. Is…

A: Seven players are playing 5-card students. Each player initially receives 5 cards from a deck of 52.…

Q: c) Let A = {x|x ES} and B = {x|x E Z; 0 < x < 6}. S is set of vowel letters and Z is set of integer…

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Q: 3.4. 1. For a set A, let P be the set of all functions from A to the two-point set {0, 1}. Then |P|…

A: To prove that |P| = |2A| P be the set of all functions from A to the two-point set {0, 1}

Q: 4. Let A be the set of citizens of the United States and let f be the function that assigns, to each…

A: Let A be the set of citizens of the United States. let ƒ be the function that assigns, to each…

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: Let A = (a, b, c), B = {b, c, d) and C = (a, b, c, d). Which one of the following alternatives…

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

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Q: 1 Using set builder notation, what is the domain for the function f(x) = A {x ER|x> 3} B {x ER | x…

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Q: Let g be the function from the set {a, b, c} to itself such that g(a) = b, g(b) = c, and g(c) = a.…

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Q: Let A = {1,2,3,4} and B = {A,B, C, D, E}. Consider the following relations and state whether…

A: A relation will be function if for each x∈A  there exists a unique b∈B with (a, b) ∈ f. In other…

Q: (a) How many functions are there from a set with three elements to a set with five elements? Imagine…

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Q: 1. Let X = {1,2} and Y = {3}, do the following. (a). Use the set-roster notation to write set (X ×…

A: Given that X=1,2Y=3 (A) To write the set X×Y×Y in set-roster notation. (B) To write two functions…

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.