Let X = {o, p, s, w}, Y = {a,b, e, g, k}, and Z = {1, 2, 3, 5, 7, 9}. Let ƒ : X → Y where f = {(o, a), (p, g),(s, e), (w, b)}. Let g: Y → Z where g = {(g, 3), (e, 2), (b, 9), (k, 7), (a, 1)}. Answer each of the following questions. (gof)(o) (gof)(s) (gof)(w) = = =

Q: 10) Show that [x] = −[−x] A 11) suppose that g: A → B and f: BC, where A = B = C = {1,2,3,4}, g =…

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Q: Let X {1,2, 3} and Y {3,4}. Define f : X → Y as follows: = f(2) = 3 and f(3) = 4. Draw an arrow…

A: We will draw the arrow diagram for function mapping from set A to set B.

Q: 21. Let f(x) = 2x, x = [0, 1]. Take P = {0, 1, 1, 1, 1, 1} and set x₁=1, x₂ = 16, x3 = 3, x4={, x3 =…

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Q: Let X = {1, 2, 3, 4, 5, 6} and let T1 = {X, 0, {3}, {1,2,3}, {2,3,4}, {2}} and T2 = {X, p, {2},…

A: T2 is a topology but T1 is not

Q: . Let C = {0, 1, 2, 3} and f : C → C, g : C → C with f = {(0, 2),(1, 2),(2, 3),(3, 0)}, g = {(0,…

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Q: 10. Let (X, Tx) and (Y, Ty) be two topological spaces, such that X = {a, b,c, d}, Tx = {0, X, {a},…

A: Definition: A function f is continuous from X to Y if inverse image of each open set in Y is open in…

Q: Q1. Let X = {m,n, p, q}, {ø, X, {p}, {m, n}, {p, q}, {m, n,p}, {q}} and Y = {a, b, c}, F =…

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Q: Given a linear map L:R-R such that L(1,0,0)=(3,-1),L(0,1,0)=(2,1),L(0,0,1)=(3,0) , then find…

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Q: Let X: = {a, b, c}. Y: = {1,2,3,4}. Let f:X → Y, f:= {(a, 3), (b, 3), (c, 4)}. If Ty = {Ø, X, {a,…

A: Let x:=a,b,c   y:=1,2,3,4   Let f:x→yf:=a,3,b,3,c,4  if Tx=ϕ,x,a,b,aTy:=ϕ,y,1,33,431,3,4   then f…

Q: Q4. Let X = {m, n, p, q}, T = {¢, X, {p}, {m, n}, {m, n, p}} and Y = {a, b, c, d}, F = {ø, X, {d},…

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Q: X = {p, q, r, s} Y = {4, 5, 6, 7, 8} The function f: X → Y is defined as: f = {(s, 8), (r, 8), (q,…

A: We want to find elements in the range of function f.

Q: 2. Let X = (a, b, c, d, e} and t = {(O, {a, c, d), (b, c, d, e), (a), (C, d), X) then subbase of (X,…

A: (2) Given a set, X=a, b, c. d, e and τ=∅, a, c, d, b, c, d, e, a, c, d, X. To find the sub-base of…

Q: (2.1) Consider the following topologies on X = {a, b, c, d} and Y = {r, y, z, w} TX = {X,0, {a} ,…

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Q: Determine the set of all z for which f(z) f(z) in u(x, y) + iv(x, y) form. 모 1-iz s defined, and…

A: We have to write in  form.

Q: Let E = {0, 2, 4, 6, ...}, define ƒ: E × E → Z¹ by the formula f(m, n) = 4m5¹, \ (m, n) € Ɛ × Ɛ.…

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Q: Find f, f, and f, and evaluate each at the given point. f(x, y, z) = x²y + 2xyz - 8yz, (-3, 1, 3)…

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Q: X = {p, q, r, s} Y = {4, 5, 6, 7, 8} The function f: X→ Y is defined as: f = {(r, 7), (s, 8), (p,…

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Q: Let X = {a, b,c, d},T= {o, X, {d}, {a,b}, {a, b, d}} and Y = (m,n, p,g},F = {@,Y, {p}, (m,n}, {m,n,…

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Q: 3. If z = f(x, y) with the relation xy²z³ + x³y?z +1 = x + y+ z. Find dz at (1, 1, 1).

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Q: Let X be the set {1, 2, 3, 4, 5, 6}, Y the set {a, ß, 7, 6}, and ƒ the map f(1) = a f(2)= a f(3) = a…

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Q: 2. Find the Domain of the given functions/relations A={(1,3),(2,4),(3,0) B={(1,2),(0,2).(5,4) D={2,…

A: Here, we have to find domain (D) and range (A) of set A and B

Q: 11. Define F:Z × Z→Z × Z as follows: For every ordered pair (a, b) of integers, F(a, b) = (2a+1, 3Ь…

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Q: Let X = {0, r, t, w}, Y = {e,g, i, k, m}, and Z = {2,3,4,5, 7,9}. Let f : X → Y where f = {(0, g),…

A: Given X = {o, r, t, w} Y = {e, g, i, k, m} Z = {2, 3, 4, 5, 7, 9}

Q: 2. Let g (x, y) = 2x² – y² . Compute 9(1, 2), g (2, 1), g (1, 1), g (–1, 1) and g (2, –1).

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Q: C is the line segment from (-1,0, 3) to (1, 3, 4), and F(x, y, z) = zi+xj+yk, evaluate Jo F.dr.

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Q: 9. Determine the intersection (if any) of the following lines: F = (-8,-5,1) + t(1,4,-1) and F =…

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Q: Q4. Let X = {m,n, pP. 9}, T = {6. X, {p}, {m, n}, {m,n.p}} and Y = {a, b, c, d}. F = {ó, X, {d}. {a,…

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Q: (b)Let A = {1,2,3}, B = {a, b, c}, and C = {x,y, z}. Consider the following %3D relations R and S…

A: Given R=1,b, 2,a, 2,cS=a,y, b,x, c,y, c,z

Q: For each of the following, determine (with argument) whether the given function T is linear. 1. The…

A: To identify which of the given function is linear transformation.

Q: Which of the following subsets of functions of the set {eª, e²ª, 2eª, 2} is linearly dependent on R?…

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Q: 10.37. Let A ={1,2,3,4}, B={a,b,c} and C = {w, x, y, z} . Consider the functions f : A → B and g: B…

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

Q: Let B = {0, 1, 2, 3} and the relations R, S, and T on Z are as follows R = {(0, 1), (1,1), (2,…

A: The given sets are -…

Q: Given the function f:{1,2,3} → N defined by f = {(1,3), (2,5), (3,1)} Is f1-1 Is fonto What is the…

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Q: Q. Let X and Y = {r, s,p,q}, F = Given the mapping f: (X,T) f(0) = r, f(1) = s, f(2) = q, f(3) =…

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Q: Let C = D = {-3, -2, -1, 1, 2, 3) and define a relation S from G to D as follows: For all (x, y) E C…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: 2. Let A = {a, b, c}, B = {x, y, z}, C = {r, s,t}. Let f : A → B and g : B → C be defined by: f =…

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Q: A {a, b, c, d} X [1, 2, 3, 4} The function f:A→X is defined by the arrow diagram below. Select the…

A: We have to select the pairs that defines a function.