Consider X = [1,2]? with the relation (x1, y1)~(x2, Y2) if x1Y2 = x2y1. Also define 3x g: X → [1,2] by the rule g(x, y) = x+y a) Write the equivalence class of (xo, Yo) E X. b) Is ga quotient map? c) Show that g is constant on equivalence classes of -. d) Show that {[(x, y)]: (x, y) E X} and [1,2] are homeomorphic.

Q: (2 1). If Let vi = 1 2 2 is ,V3 V4 3 a dependence relation on (v1, v2, V3, V4) thenx = a) 17 b) 15…

A: Here, we have v1=111, v2=123, v3=321, v4=210. If xy-1-3 is a dependence relation on v1, v2, v3, v4,…

Q: Consider the relation R on the set of functions defined by (f, g) = R if and only if f(x) is…

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Q: Consider the relation R = {(a, b) ∈ Z × Z : 3a − 5b is even }. Show that R is an equivalence…

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Q: Consider a linear map T: U → R² and uí, u₂ € U. Given that T (u) = (-3,6) and T ԱՉ mapped to (0, 0)…

A: Given: Tu1→=-3,6T ; Tu2→=5,-10T.We need to find the vector which is mapped to 0,0T.

Q: be the map O Let f Sending cach Complex number

A: The detailed solution is as follows below :

Q: 7.4.3 Let X = {1,2,3}. Define the relation R = {(1, 1), (1,2), (1,3), (2, 1), (2, 2), (3, 1), (3,3)}…

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Q: 1. for  the Relation R ‘is a factor of’, on set A{1,2,3,6}. Write: A) the ordered pairs B) a…

A: Given the set A{1,2,3,6}

Q: Let A = {1,2,3}, X = {1,3}, and R is a relation on A, such that R= {(x,y) | x<y^x, y = A} R"X =…

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Q: (i) Let A = {-1, 1,2,3,4}, X = {(-1, 1), (1, 1), (2, 2), (3, 3), (4, 4), (1, −1), (1, 4), (4, 1)}.…

A: We are allowed to do a maximum three sub parts as per bartleby guidelines

Q: Let C denote the set of all ordered pairs (a, b) with a,b & R. L.e., C:= {(a,b): a,b € R}. Define…

A: NOTE: According to guideline answer of first three related subpart can be given, for other please…

Q: Let A ={1, 2}, B = {1, 2, 3} define a relation R from A to B given any {x, y} ϵ A cross B.…

A: A=1, 2, B=1, 2, 3 R is a relation defined as R=x, y: x+y2 is an integer.

Q: (b) Let R= {(x,y) E R × R : 1 < x < 4 or x = 6}, %3D and S = {(x, y) E R × R: –1< y < 1}. i. Find…

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Q: Consider the three basic vectors: (2,1,0,-1),(-1,1,1,1),(2,7,4,1) a. give two vectors that are in…

A: Given the three basic vectors:                           (2,1,0,-1),(-1,1,1,1),and (2,7,4,1) We have…

Q: Define a bijective map g : x2/3--->R.

A: Sol

Q: Please help me out

A: Equivalence Classes: The set S is divided into equivalence classes by ~, which is an equivalence…

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: Assume (r1, y1) ~ (x2, Y2) → f(x1,Y1) = f(x2, Y2). Prove that ~ an equivalence relation.

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Q: Please find a relation R that makes the statement true and a relation R(x, y) that makes the…

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Q: V = Span{(1, 2, 3), (1, 0, 2)} and W = Span {(0, 2, 1), (1, 1, 1)}. Find the relation between V and…

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Q: Consider the relation R on R2 given by for any (a,b),(c,d)∈R 2, (a,b)R(c,d) if and only if a 2 +b…

A: According to the given information, Consider a relation R on R2 as:

Q: 1. L: V3 V4 defined by L(a, b, c) = (a - b,b+c-d, a+b-2d, b-c-d) 2. L: V4 → V3 defined by L(a, b, c,…

A: According to Bartleby guidelines we can only solve 1 question or three subparts. So put other one…

Q: For the points (x1, y1) and (x2, y2) in the plane R?let (x1, y1)~ (x2,Y2) mean that xỉ + yỉ = x + y…

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Q: R= {(0,2). (1, 1). (1,3), (2, 1). (2, 2). (2,3 For relation R find the Reflexive closure; Symmetric…

A: Given:- Set A={0,1,2,3}   , relation R:A×A is defined as : R={…

Q: Let R be the relation on Z given by R= {(a,b) : a < b}. %3D (a) Find R-1. (b) Find R which is Z x Z…

A: relation on Z.

Q: Let R be the relation on the set (0, 1, 2, 3} and R= {(0, 1), (1, 1), (1, 2), (2, 0), (2, 2), (3,…

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Q: Q-3: a) Let R be a relation on A = {1,2,3,4} such that aRb means |ab| ≤ 1. Find the matrix…

A: (a) It is given that, R be a relation on A = {1, 2, 3, 4} such that aRb ⇔ a-b≤1 We have to find the…

Q: Use only the definition of affine dependence to show that an indexed set {v1, v} in R" is affinely…

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Q: 4. Define a relation R on the x-y plane as follows: Given two points (X₁,Y₁) and (x2,Y2) in the x-y…

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Q: (b) Let X=ZX (Z \ {0}). Define the relation = on X by (x, y) = (z,t) ⇒xt = yz for every (x, y),…

A: Given: Let X=ℤ×ℤ \ 0. Define the relation ≡ on X by  x,y≡z,t⇔xt=yz for every x,y, z,t∈X. To prove:…

Q: Let us define a relation S on R3: If p1 = (x1, y1, z1) and p2 = (x2, y2, z2) are two points in R3,…

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Q: A relation R on a set A is called irreflexive iff (Vx E A)((x, x) ¢ R). It is called asymmetric iff…

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Q: Show that the mapping f:R2 → R² defined by f(x1, x2) 5x2) is linear. = (2x1 + x2, -3x1 +

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Q: Let A = {1,2,3}, X = {1,3}, and R is a relation on A, such that R= {(x,y) | x<y ^ x, y = A} R"X =…

A: , and is a relation on .

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 fi = 1+a +x², f2 = 3 + 2x +x², f3 = 1+2x + 3x², fa = 1+3r + 5æ². If is a dependence relation on…

A: We have to solve given problem:

Q: Prove that these relations on the set of all functions from Z to Z are equiva- lence relations.…

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Q: Draw the diagraph of the relation R, where the relation R on {1,2,3,4} defined by (x,y) ∊ R if x^2…

A: