A relation consists of all the points in the x-y plane that are either on the line y=1 or the line y=x is this a function l? Why or why not?

Q: Which is not true with the descriptions of a function? *       a. A function is also a relation.…

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Q: 9. The mapping shows a relationship between x and y. y is not a function of x, since the y-value 3…

A: Given: A mapping showing the relation between x & y To determine: y is a function of x or not.

Q: Describe the domain and range of the function. f(x, у) - 8x2 - у Domain: o {u, v: v z 0} o {x, n): *…

A: Given that: f(x, y)=8x2-y

Q: Find all points of discontinuity for the föllowing 3 x 2 +6 f(x)3D x 2-7 x+12

A: SOLUTION-

Q: 2. Use first differences, second differences, and/or ratios to classify each relation as linear,…

A: a) Here, from the given table we find the ratios of the consecutive terms: x y Approx. Ratio -3…

Q: (a) Show that the following sentence ¬Vz(3yR(x,y) = R(x, f(x, x)) is satisfiable where f is a…

A: a)

Q: termine the domain and range for the relation. R = {(x, y)|x E Z and y = 2x} %3D swer Domain OR ON…

A: We have to find domain

Q: Describe the domain and range (i.e., comment on whether the domain and range are bounded/unbounded…

A: Consider the given function: fx,y=lnx2+y2 Find the domain: Domain is the set of input value where…

Q: Prove this is an equivalece relation. x related to y iff x2 -  y2 is even

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Q: Let f(x, y) = x° /Y Evaluate f(5, 1)

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Q: For a function f: A --> B and subsets C and D of A and E and F of B, prove that the relationship is…

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

A: given sets  A= 1 , 2 , 3 , 4B=4 , 6 , 8 , 10relation  H =x,y∈ A×B : x+1=y2

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: 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…

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Q: c) In this problem sheet, we will call a relation geometric if Vr, y, z(1Ry A IRz → yRz) i) Prove…

A: PART (i) Let R is a relation which is geometric and reflexive. Now xRy , Now xRx because R is…

Q: (i) Give an example of a relation S on A = {1,2, 3, 4} with S is reflexive, not symmetric and not…

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Q: Let the relation S defined as S = {(x,y) | y = X2 + 4x +3}. What is the domain of S?

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Q: The inverse of a relation r is r {(0, 0), (0, 1), (0, 2) }. Which of the following may be the…

A: Topic = Relation   The Inverse of a Relation is a set of ordered pairs that is the exact inverse of…

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 =…

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Q: 16. A is the “absolute value" relation on R: For all real numbers x and y, x A y → |x| = |y].

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Q: (a) Show that the formula (VæR(g(x), x) = Vx3yR(y,x)) is universally valid, where g is a 1-place…

A: Part(a): As we know, ∀xRgx,x⇒∀x∃yRy,x Where g is a two place function symbol and R is a two place…

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: 2. Consider the function ƒ : R × R –→R x R defined by Determine the powers of f. (Note that R × R…

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Q: find and sketch the domain of the function f(x,y)= Suqare root 2x-y

A: f(x,y)=2x-yAs we know that domain refer to set of positive values  while range is the set of…

Q: i). Find the highest normal form of a relation R(A,B,C,D,E) with FD set as (BC->D, AC->BE, B->E}

A: As we can see, (AC)+ = {A, C, B, E, D} but none of its subset can determine all attribute of…

Q: A = [a,b), be an (right half-open) interval of R. 6 (c) (d) a,be R+,b+00, Explain whether f(A) is…

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Q: A set of points in the xy-plane is the graph of a function ifand only if every________ line…

A: A function relates inputs to output . An expression is called function if it gives different outputs…

Q: True or False A function is a relation between two sets Dand R so that each element x in the first…

A: By definition: A function is a relation from a set of inputs to a set of possible outputs where each…

Q: 1. State the domain of this relation. * 2 -2 {x ɛR} O {x ɛ R, x + 1} O {y ɛ R} O {y ɛ R, x + 1}

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Q: Determine whether Rolle's theorem can be applied to f on the closed interval [a,b]. If Rolle's…

A: Given: f(x)=x2-2x-3x+2 The given interval is:a,b=-1,3 Condition for Roll's theorem: 1) f(x) is…

Q: Given that A = {1, 2, 3, 4, 5} and B = {x, y, z}, determine which of the sets of ordered pairs…

A: 1.  i) This ordered pair doesn't represents a function because the values 'y' corresponding to x= 4…

Q: Which of the relation defines a function from X=(2,4,5) to Y=(1,2,4,6). R1 = {(2,4), (4,1)) R2 =…

A: We have to determine which of the following defines a function from X=2, 4, 5 to Y=1, 2, 4, 6. R1=2,…

Q: Find a function from the set {1,2,.....30} to {1,2,.....10} that is a 3-to-one correspondence.

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Q: 11. Define a relation P from R to R as follows: For all real numbers x and y with x>0, (x, y)e P…

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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: 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: The relation is a subset of the cartesian product of any two sets A and B. The function is a special…

Q: Let f(x, y) : = x/Y Evaluate f(3, 4)

A: We need to evaluate f(3,4) To evaluate we need to plug in 3 for x  and 4 for y

Q: - SAT/ACT For a relation, where y is a function of X, and y = 4 vwhen x = 6; which of the following…

A: Definition: A relation is said to be function if each element in domain is mapping to a unique…

Q: 5. Find three relation from {1, 2} to {6, 7} that are NOT functions.

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

Q: Let X= {a, b, c} and Y= {1, 2, 3, 4}. Which of the relations A, B, C defined below are functions…

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Q: Evaluate the function at the specified points. f(x, y) = x + yx“, (-5, 5) , (2, 5) , (–5, –2) At…

A: Given: f(x, y)=x+yx4, (-5, 5), (2, 5), (-5, -2)

Q: 5. Let f, and f, be the function from R to R such that f,(x) = x²+2x+3 and f,(x) = x-x. What are the…

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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…

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

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Q: Define a relation Pfrom R+ to R as follows: For all real numbers x and y with x> 0, (x, y)E P means…

A: Introduction: A relation is a subset of Cartesian products of two sets. In each ordered pair, there…

Q: What is the domain of the function y = h(r) = V2r+1 ? All values of r in the set [0 ,+). All values…

A: Here the function given is y=hr=2r+1r.

Q: If X = {-2,-1 ,0 ,1,2} and Y = {4 ,2 ,, } and R is a relation from X to Y where "a R b" means "b 2"…

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Q: A relation R on A = {1,2, 3, 4} is defined by x R y x² – y? < 0. (i) List all the ordered pairs that…

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Q: The following ordered pairs (z, y) define the relation Q. Q= {(-1,4), (-2, 3), (4, 4), (2, – 2)} Is…

A: Given relation is  Q=−1,4,−2,3,4,4,2,−2