QUESTION 11 Let x = {1,2,3,4,5,6} and y = {a,b.c,d,e.f} Which of the following functions is not onto? O fi= {(1,b),(2,c),(3,d),(4,a),(5,e),(6,c)} cX xY O f2= {(1,a),(2,b),(3,c),(4,d),(5,e),(6,)} cX xY O fa= {(1,f),(2,e),(3,d).(4,c),(5,b),(6,a)} cX xY O f3 = {(1,b),(2,d),(3,a),(4.).(5,c).(6,e)} cX xY

Q: Prove that there does not exist any function f(x, y) such that

A: To show that there does not exist any function that satisfies the given conditions

Q: 1. Let A = {a, b, c}, B = {1,2,3}, C = {x, y, z, w}, D = {4,5, 6}. Let the functions f : A → B, g :…

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Q: Let A = {1, 3, 5, 6, 7, 9, 10, 12} and B = {1, 2, 3, 5, 7, 8, 9, 11, 12}. Consider the following…

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Q: A = {1,2,3}, B = {4,5,6}, C = {7,8,9,10} define the functions f :A→C and g:B→C by f(1) = 7, f(2) =…

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Q: (2.1) Let h: Z → Z be a function given by h = |r|, Va € Z. Show that (a) h is not one-to-one (b) h…

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Q: Let A and B be two sets and f be function. f: A B.Assuming the function f is invertible, what is the…

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

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Q: Question 4. Consider the functions f : A→ B, g : B → A andh: B → A such that if gf = 14 and fh = 1g.…

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Q: Compute the following values for the given function. uevw + veuw + weuv VW g(u, v, w) u2 + v2 + w?…

A: See attached file for a step by step explanation.

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Q: Let f(x, y) = (2x - y,x-2y); (x, y) E R x R, (R is set of real numbers.) %3D a) Show that f is one…

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Q: 1 Jigull (a,b,c, d} determine which of the following relations is a function fron X to Y:…

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Q: 10. Determine whether each of these functions from {a, b, c, d} to itself is one-to-one. a) f(a) =…

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Q: Let f be the function from {a, b, c} to {1, 2, 3} such that f (a) = 2, f (b) = 3, and f (c) = 1. Is…

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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 = {(s, 8), (r, 8), (q,…

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Q: Question 4. Consider the functions f: A → B, g : B → A and h : B → A such that if gf = 1 4 and fh…

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Q: Let f : {1, 2, 3} → {a, b, c} be one-one and onto function given by f(1) = a,   f(2) = b and f(3) =…

A: Consider

Q: 2. Let N = {1,2,3,...}. Are the following functions injective, surjective and/or bijec- tive? (i) f:…

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Q: Given F(A, B, C, D) = A'B'C'D' + A'B'C'D + A'BCD' + A'BCD, express F(A,B,C,D) and F '(A,B,C,D) in…

A: Solution: Given that F(A, B, C, D) = A'B'C'D' + A'B'C'D + A'BCD' + A'BCD Now, truth table Row no.…

Q: QUESTION 9 Which functions on (1, 2, 3, 4) × {a, b, c) is NOT onto? O {(1, c), (2, a), (3, a), (4,…

A: Identity function

Q: A = {2, 3, 4, 5} and B et f : A → B be a func ow. Which of the following

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Q: Let A = (1, 2, 3, 4, 5) and B = {a, b, c) and f = {(1, a), (2, a), (3, b), (4, b). (5, b)}. Choose…

A: Given. (a) f is a onto function because image of 1 and 2 are same also image of 3, 4 , 5 is same.…

Q: Let W(s,t) F(u(s, t), v(s, t)) where u(1,0)-4, u,(1,0) 3, u(1,0)- 5 v(1,0) 7, v.(1,0)=-3, v(1,0)--6…

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Q: 15. Show that if f: A- 1 f(GnH)=f(G) B and G, H are subsets of B, then f-¹(GUH)=f(G) Uf (H) and nf…

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Q: Let R(s, t) = G(u(s, t), v(s, t)), where G, u, and v are differentiable, and the following applies.…

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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: Determine whether cach of these functions from Z to Z is one-to-one. a) f(n)=n- I c) f(n)=n b) f(n)…

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

Q: 18. Let A = {1,2, 3}, B = f: A → B, and g : B → C, such that {W, Y, Z}, C = {7, V2, V5}. Find…

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Q: Let f be the function {(1,4), (2, 1), (3, 3), (4, 2)} and g be the function {(1,3), (2, 4), (3, 2),…

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Q: Let A={1, 2, 3, 4, 5} and B={a, e, i, o, u}. If ƒ: B → A is a function defined by f ={(a, 4), (u,…

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Q: Which functions on {1, 2, 3, 4} x {a, b, c} is NOT onto? О {1, с). (2, а). (3, b). (4, b)} О {(1,…

A: Given sets are {1,2,3,4} and {a,b,c}. We know that a function f from A to B is called onto if for…

Q: If f:{1,2,3}->{a,b}, f(1)=a f(2)=b f(3)=a then explain why f is onto but not one to one

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Q: If f is a function from X to Y and A, B are subsets of X then .A f(A – B) = f(A) – f(B) .B f(AUB) =…

A: Given: f:X→Y and a,b⊆X, Find out: To choose the correct option.

Q: Given the function f , g and h, all with source and target {1, 2, 3, 4}, defined as follows: f…

A: 1. g(2)= 3 2. f (f (4))= 1 3. g (h(4))= not defined.

Q: Exercise 2. Let f : A → B be a function with Y1 and Y2 subsets of B. Prove that if Y1 C Y2, then…

A: Let f:A→B be a function and let Y1,Y2⊆B. Suppose that Y1⊆Y2 To show f-1(Y1)⊆f-1(Y2) Let x∈f-1(Y1)…

Q: Let W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable, and the following applies.…

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Q: Write the following function as a subset of the Cartesian product of the domain and codomain. 2. 3.…

A: Given,

Q: 1. Let A={1,3,5,7}. Let f:A→Z be the function f={(1,2),(3,4),(5,6),(7,8)}. Let g:Z→Z be defined by…

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Q: 2.4. Let J and J be real valued functions defined on a subset of a linear space Y, and suppose that…

A: We will use basic knowledge from the theory of calculus of variations to answer this question. You…