Let X = {o, s, v}, Y = {c, d, e, i}, and Z= {0, 3, 6, 8, 9}. Let f : X → Y where f = {(o, c), (s, e), (v, d)}. Let g: Y→ Z where g = {(e, 9), (c, 8), (d, 3), (i, 6)} . g • f = { }.

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

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Q: 4. (a) Let A € R² be open and let f: AR be C². Let (a, b) A and suppose the rectangle R= [a, a +h] x…

A: (a) Since f, using Mean value theroem w.r.t. x for two variables there exists a pR such that f(a +…

Q: Evaluate e fry²dæ + x³dy, where C' is the rectangle with vertices (0,0), (4,0), (4,2), and (0,2)

A: We apply the green's theorem to solve the given problem.

Q: In → C A Os B CS C+ 0x www.awu.aleks.com/alekscgi/x/sl.exe/1o…

A: To solve the problem of finding the domain and range of the piecewise function shown in the graph,…

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: 6. Let u = (1, 2, –3) and v = (4,0, –2). Compute u x v. 7. Let u = (2, 4, -4) and v = (1, –3, 1).…

A: Used vector cross product

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: get the following sets {(x, y) : x ∈[1, 2], y ∈[1, 2]} and {(x, y) : x = 2, y ∈[0, 1]}

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Q: 5. If r = (r, (x, y, z) and ro = (xo, Yo, 20), describe precisely the set of all points (r, y, z)…

A: We plug the given values in the given equation and simplify

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: 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,…

A:

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: Suppose g : A → B and f : B → C where: А 3D {а, b, с, d}, В 3 {1, 2, 3}, С%3D {e, h, g, k}, and g…

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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: Given u = (0,1, -1,2) and v = (1,1,3,0) find ||u + v||

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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: Let A, BCR x R defined by A= {{n,m)|n, m € N, 0 < 2m(n + 1) – 3 < 5}, and B = {(1,1), (1,2), (2, 1),…

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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: 8. For each of the functions below, indicate whether the function is onto, one-to-one, neither or…

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Q: Let A = {1, 2, 3}, B= {4,5,6, 7} If f: A x B → N with f((a, b) = b – a , find the following. a. f…

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Q: 4. Let L: R² → R? be a linear operator. If L((1, 2)") = (-2, 3)" and L((1, – 1)") = (5, 2)" find the…

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Q: Let U = {1,2,3,4,5,6,7,8,9); X= {2,4,6,8}; Y={2,3,4,5,6}; Z={1,2,3,8,9} XnY X' Yn(XuZ) (XnY') u…

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Q: U is a neighborhood of x0 and U ⊂ V, The V is a neighborhood of x0. (2) If U1 ...., U2 are…

A: Solution ::