Let X = {a} and y = {a, b}, do the following. (a). Use the set-roster notation to write set (X x X) x Y. (b). Find two functions and two non-function relations from X xY to Y.

Q: Let x1, x2, y1, y2 be real numbers. The expression (x1, y1) ~ (x2, y2) means that x12 + y12 = x22 +…

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Q: Determine if the relation ? = {(f, g)|f(x) = g(x) for some x ∈ ℝ} on the set of all functions from ℝ…

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Q: Give the domain of each function, written in set-builder notation, and also sketched in the…

A: The objective is to give the domain of the function written in set builder notation and also sketch…

Q: Let A and B are nonempty sets, and functionƒ maps A to B. Which of the sets below is the rang of the…

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Q: Suppose that R1 and R2 are symmetric relations on a set A. a) Is R1 U R2 also reflexive? Is R1 ∩ R2…

A: Let A be any set with  symmetric relations R1 and R2 defined on it. Hence R1 and R2 be subset of…

Q: Give an example of a relation on the set {a, b, c, d} which is symmetric and transitive, but not…

A: Any relation R from a set Ato A is reflexive if and only if for every x∈A , the pair (x,x)∈R Any…

Q: Determine whether the given relation is reflexive, symmetric, transitive and an equivalence…

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Q: Which among the folowing reletions are considered as functions? (You need to choose all the ccrrect…

A: Find your answer below

Q: Determine whether the given relation is reflexive, symmetric, transitive and an equivalence…

A: By definition of  relation it is define as A relation is symmetric if and only if (b, a) ∈ R…

Q: If R is reflexive, symmetric and transitive then the relation is said to be--------

A: Any relation R on a set S is equivalent if and only if it follows the below conditions: (a) R is…

Q: For each relation, decide whether or not that relation is reflexive, symmetric, antisymmetric or…

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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: Describe the equivalence classes of the relation R = {(a, b) : a € Z, b E Z, 13 divides (a – b)}

A: a equivalence class is a subset of the set on which the relation R is defined such that all elements…

Q: For each relation F, indicate if it is: reflexive, anti-reflexive, or neither; symmetric, anti-…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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: Select any and all statements that correctly describe this relation. Input Output 2 20 30 40 4- 3.

A: Our Aim is to describe the correct relation between input and output byexamining all the…

Q: What is the domain of the relation x(x-3) ? {(X,y): y = (x+4)(x-7)). ) {x: x = R, x -4, x > 7} ) {x:…

A: Domain of function f(x) is the set of value of x for which f(x) is defined.

Q: On sets, the relation x R y given by there exists a bijective function from the set x to the set y'…

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Q: Every function is a relation of its domain and codomain. O True. O False.

A: A relation defined between two sets X and Y contains ordered pair a,b such that  a∈X ,  b∈Y. It…

Q: Let C and D be finite sets and let f: C D and g: D C be two functions such that Vy eD f(g(y)) = y…

A: If there exists an one-one map from D to C then "|D| < |C|" or "|C| >|D|".

Q: Let S be the set of all real numbers and let R be a relation in S, defined by R = {(a, b) : a < b³}.…

A: Given relation is R = {(a, b) : a ≤ b3}

Q: Give an example of a function f : (X1, d1) → (X2, d2) that sends compact sets to compact sets, but…

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Q: Consider the relation R = {(a, b), (a, c), (c, c), (b, b), (c, b), (b, c)}. Is R reflexive,…

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Q: A relation that assigns to each element x from a set of inputs, or ________, exactly one element y…

A: To fill: The blanks of statement: Given: The statement is "A relation that assigns to each element x…

Q: Consider the relation R = {(a, b), (a, c), (c, b), (b, c)} on the set A = {a, b, c}. Is R reflexive,…

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Q: Let C and D be finite sets and let f :C → D and g : D →C be two functions such that Vy ED f(g(y)) =…

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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: Directions: Identify the domain for each relation using the set builder notation. 1. y 5x-4 6. g(x)…

A: Given equation of the function is: y = 5x - 4

Q: Je fine a binary relation Rond by R= [(y)] ER² x ус

A: Given is : R={(x,y)}∈R2:x-y∈Q We have to show that it is an equivalence relation.

Q: Suppose that the relation T is defined as follows. T = {(2,b), (7,0), (4,2), (7,a)} Give 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: Express the set W = {q|q 2} using interval notation. Use "U" for or .

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Q: Determine if the relation defines y as a ône-to

A: The given graph is: To determine if it is one-to-one.

Q: Define a relation D on the set of real of numbers as follows: Vx, y ≤ R, x Dy x-y is rational ⇒…

A: Definitions of symmetric, reflexive,transitive are given.We have to check them .

Q: Let A, B, and C be nonempty sets and let f: A -> B, g: B -> C and h: B -> C be functions. Find a…

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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: Let T be the relation in the set of real numbers IR defined by xTy of both xe [n, n+1] and ye[nin+1]…

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Q: Define a relation ~ on the set of real numbers by X~ y means | x |+|y|=|x+y|. Determine whether - is…

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Q: List the coordinate pairs needed in order to turn the following relations into equivalence…

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Q: (a) Explain what it means for a relation R on a set S to be (i) reflexive; (ii) symmetric; (iii)…

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Q: Give an example of a relation over the set {0, 1, 2, 3} that is not reflexive, not symmetric, and…

A: We need to give an example of a relation over the set {0, 1, 2, 3} that is not reflexive, not…

Q: Define a relation on Z x Z, xRy, |x - y| < 1. Is R reflexive, symmetric, and/or transitive? Explain…

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Q: Show that if for a relation R we know that R^2 ⊆ R, then R is transitive, and conversely.

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Q: A car dealership sells cars that were made in 2015 through 2020. Let the cars for sale be the domain…

A: Given

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

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Q: R How to prove that " If is the equivalence B relation on the set and is the function R = IB then

A: given in question R is a equivalence relation on set B that means R is reflexive ,transitive  and…

Q: Is the set θ={((x,y),(3y,2x,x+y)) : x,y∈R} a function? If so, what is its domain and range? What can…

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Q: prove why each relation has or does not have the properties: reflexive, symmetric, anti-symmetric,…

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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…