IF A = { 1,1,2,3,5} B = {2,4} A relation S from A to B such that (x, y) ∈ S means that x ≤ 3 and y > 2 and determine if S is a function or not. Defend your answer by stating a definition.

Q: Consider the set ℕ× ℕ. We will informally think of the pair (x, y) ∈ ℕ× ℕ as representing the…

A: a) The relation is defined on ℕ×ℕ as follows. x,y~n,m if and only if x+m=n+y. Every x,y~x,y since…

Q: 0,1,2

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Q: Answer with True or False. 1. The functions from Z to Z is onto if f(n)=n−1. 2. These function…

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Q: If In (x² - y) -x+y+1 then the domain D of the function f is given by the set Select one: f(x, y) =…

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Q: Let A = {0, 1, 2} and B = {1, 2, 3}. If an element x in A is related to an element y in B iff x = y…

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Q: Define the following relations on A = {0, 1,2, 4}. Answer each of the following questions by listing…

A: We will use the basic definitions

Q: Let A = {x, y} and let S be the set of all strings over A. Define a relation C from S to S as…

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Q: Let {2,3,4}{2,3,4} and {8,9,10}. Define a relation H from A to B such that (x,y) ∈ H if and only if…

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Q: Let f: X → Y and define x~y if f (x) = f (y). Show that - is an equivalence relation on X.

A: The objective is to show that ~ is an equivalence relation on X.

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

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Q: 2) Define a relation R from {a, b, c} to {u, v} as follows: R = {(a, v),(b, u),(b, v),(c, u)}. a)…

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Q: Suppose that the functions u and w are defined as follows. u (x) =-x+2 w (x) = -2x? Find the…

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Q: Suppose that the functions q and r are defined as follows; u(x)= x-1 w(x)= -2x2+2 (w °u) (2)= (u…

A: Given functions: ux=x-1w(x)=-2x2+2

Q: Let Y = {0,1,2} and Z = {0,1} and define a relation R from Z to Y as follows: Given {x, y} € Z x Y,…

A: Relation : A relation between two sets is a collection of ordered pairs containing one object from…

Q: a. If f(x,y) is convex with respect to (x,y) and C is a convex set, show that g(x) = infyec f(x,y)…

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Q: For a function g(x), if there exists x E[a,b] such that g'(x)> 1, then we conclude that g(x) has not…

A: For a function g(x), if there exists x∈[a,b] such that g'(x)> 1, then we conclude that g(x) has…

Q: . Define a relation from Z to Z as follows: For all x EZ and all y E Z, x and y are related iff y =…

A:

Q: Define a relation C from R to R as follows: For any(x, y) ∈ R × R, (x, y) ∈ means that x2 + y2 = 4…

A: Topic = function

Q: A function F from a set A to a set B is a relation with domain A and co-domain B that satisfies the…

A: Relation: Let A  and B  be two sets then relation between A nd B means  the collection of the…

Q: The function f is defined as follows: f: R2 R2 with f(x, y) = (2x, x+y) Which statement is correct?…

A: Disclaimer: Since you have asked multiple question, we will solve the first question for you. If you…

Q: Let X-(3, 4, 6, 8). Determine whether or not the relation R = {(x, f(x)) :x - X, f(x) %3D = x2 + 1}…

A: Solution is given as: Hope the answer is helpful.

Q: Let A = {0,1,2} and B = {-2,-1,0}. Define a relation C from A to B as follows: For any (x,y) A x B,…

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Q: Prove that the following relation from Z= {c, o, u, n, t, r, y} to X= {h, a, z, k}is a onto but not…

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Q: Let G = {-2,0, 2} and H = {4,6,8} and define a relation V from G to H as follows: %3D For all (x, y)…

A: Solve the following

Q: Suppose that the function h is defined on the interval (-2, 2 as follows. (-1 if -2<rs-1 if –1 <x<0…

A: Solve the function

Q: Let R be a relation on the set of all functions from Z to Z defined by: R = {(f,9)|f(1) = g(3) or…

A:

Q: Let A = { 1, 2, 3, 4 } and B = { 4, 6, 8, 10 }. Define a relation G from A x B as: For all (x, y) ∈…

A: Recall: If A and B are two sets , then a function from A to B is a rule that assigns to each…

Q: 5. 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: Define a relation C from R to R as follows: For any (x, y)  £ R x R.  (x, y)  C means that x² + y²…

A: Given: Define a relation C from R to R as follows,for any (x,y)∈R×R (x,y) C means that x2+y2=4

Q: Let {2,3,4} {2,3,4} and {8,9,10} {8,9,10}. Define a relation H from A to B such that (x,y)∈H(x,y)∈H…

A: Given A={2,3,4} B={8,9,10}

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) –…

A:

Q: Let G = {-2, 0, 2} and H = {4, 6, 8} and define a relation V from G to H as follows. For every (x,…

A: Given,            G=-2, 0, 2  and   H=4, 6, 8and  define a relation v from G to H as follows.For…

Q: The function f is defined as follows: f: R² R² with f(x, y) = (2x, x+y) Which statement is correct?…

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Q: Suppose that the functions u and w are defined as follows. u (x) = x² +9 w (x) = /x+ 8 Find the…

A: To find the functions

Q: Suppose that the functions u and w are defined as follows. u (x) = - 2x+1 w (x) = 2x2 – 1 Find the…

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Q: Let f : X → Y be a function. Define a relation R in X given byR = {(a, b): f(a) = f(b)}. Examine…

A: Given:

Q: Let G = { -2, 0, 2} and H = {4, 6, 8} and define a relation V from G to H as follows: For all (x, y)…

A:

Q: Given x = {5,10,15,20,25,30} and y function from X to Y. Let f(5) = 400, f(10) = 100, f(15) = 500, f…

A: x=5, 10, 15, 20, 25, 30  &amp;  y=100, 200, 300, 400, 500, 600. f5=400,  f10=100,  f15=500,…

Q: Assume that the relation In (x"z°12) +6(x- 1)y + 512xz + 729y°z =0 defines y implicitly as a…

A: Given:yx,z=x10z512+6x-1y+512xz+729y3z=0To find:  dydz at x,z=1,-1

Q: Define a relation P from R to R as follows.for all real numbers X and Y with X>0 (X,Y)€P means that…

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Q: Define the following relations on A = {0, 1,2,4}. Answer each of the following questions by listing…

A: I am going to solve the given problem by using some simple algebra to get the required result of the…

Q: 7. Define a relation M from R to R as follows: For all real numbers x and y, (x, y) e M means that y…

A:

Q: Let Y = {0,1,2} and Z = {0,1} and define a relation R from Z to Y as follows: Given {x, y} € Z × Y,…

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Q: Determine the domain and range of the relation R defined byR = {(x, x + 5) : x ∈ {0, 1, 2, 3, 4,…

A: We make a table for the relation x x+5 0 5 1 6 2 7 3 8 4 9 5 10

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: Let X = {x € Z+ | 15 < 4x < 22} and Y = {y is even | 0 < 2y +1< 15}. Define a relation R from X to Y…

A: ANSWER ONLY ASAP! What are the elements of the Cartesian product X x Y?

Q: Let A = {2, 4} and B = {1, 3, 5} and define relations U, V, and W from A to B as follo %3D For every…

A: A function from a set X to a set Y is an assignment of an element of Y to each element of X. The set…

Q: If In (x² - y) √-x+y+1 then the domain D of the function f is given by the set f(x, y) = Select one:…

A:

Q: Let A = {2, 4} and B = {1, 3, 5} and define relations U, V, and W from A to B as follows: For all…

A: It is given that (x, y) is in U if and only if y-x≥1. Now, for every x in A, we find the values of y…