5. Consider the permutations 1234 2 1 3 4 on the set {1, 2, 3, 4). Find fog and go f. (a) (b) F Find f, and verify that ƒoƒ-¹ (c) () Find g¹, and verify that 1 gog-¹- - and g = 1 2 3 4 3142 1 2 3 4 1234 1 2 3 4 1234 1) = 5¹ of =g-log

Q: 7. (10 points) Let f: A B be onto. Prove that S((C)) = C for all sets CC B.

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Q: 1. If f is a function on a set A = {1,2,3,4,5} such that f = {(1,2), (2,3), (3,4), (4, x), (5,5)}.…

A: Answer C

Q: With f = {(0,6), (1,3), (4,7), (5,8)} and g = {(-1, 2), (1, 4) , (2,3), (4,8)) Determines: A) f +…

A: Given f = {(0,6), (1,3), (4,7), (5,8)} and g = {(-1, 2), (1, 4) , (2,3), (4,8)) The domain of f =…

Q: U = { all real numbers} A = { 10, 11, 12, 13, 14, ...} B = {-3, -2, -1, 0, 1, 2, 3} C = {-1, -2,…

A: This is a problem related to set theory. Based on the general formula we will answer the question.…

Q: 7. If F{f} = [1, 1+ i, –2i, 2i, 1– i] then compute F{f©f}.

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Q: 1. A₁-[0,4], A2-[1,5), A3= [0.5,3], A4- (1,9] As 2. A₁-[0,4], A₂-[1,5), A3- [0.5,3], A- (1,9] As 3.…

A: Given- Ω=set of all real numbers  A= index set  To identify the generalized union and intersection…

Q: Determine if 0 >=(61-6-J-RA) is in the span of = 0

A: Given: -1225 To check:If -1225 is in the span of Φ=1100, 1001, 0110, 0011 or not.

Q: Determine if [23] is in the span of = (3-69-81-])

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Q: ›) Prove that if the function ƒ is 1-1, then ƒ−¹ is a function. Caution! The ONLY assumptions here…

A: We use definition of function and one-one function to prove that f-1 is function.

Q: Dijec not need to prove you function is a bijection): (a) N and Z (b) Rand (1, ∞) (c) (0, 2) and (3,…

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Q: suppose g: A---> B and f: B---> C  are both one-to-one. prove f o g is one-to-one

A:

Q: 6. Let F = (-6, 5)U{-10, 10} U [7, 11). Find max F, min F, sup F, and inf F if they exist.

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Q: Which of the following sets spans R? R32 O (3,0,-2)} O(3,0-2).(0,0,0)} O(3,0,-2).(5,1,0),(0,-1,1)} O…

A: hello greetings from bartelby.i am here to help you.

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

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Q: Let A = {1, 3, 5, 7, 9, 11}, B= {a, b, c, d, e}, and ƒ be the function from A to B defined as below:…

A:

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: Let Ω-set of all real numbers, A-index set. Identify the generalized union and intersection of the…

A: Given: Ω set of all real numbers To find: Solution

Q: Show that a,b,c are in A.P. If x is the G M be tween a and b and y is the G M between b and c,  then…

A: We have to show if  a, b, c are in A.P.,  x is the G M be tween a and b and y is the G M between b…

Q: Let f and g be permutations. Show that the order of h=fgf^−1 is the same as the order of g.

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Q: 3. A = {2, 2+2, 2+4,2+6, 2+8} where A = {2,4,6,8} 4. A=(1-22, 1+22) where A = Z*

A: Note : (i) ∩α∈S Aα=x : ∀α∈S ,x ∈Aα               (ii) ∪α∈S Aα=x : ∃α∈S ,x ∈Aα

Q: Then, there exists k1≠0, k2≠0  such that a,b=k1c,k1d   and  c,d=k2e,k2f. a,b=k1c,d=k1k2e,…

A:

Q: -16] --14] Let ai -20|, a2 = -16 and az = –18 -4 -4 -4 The set {a1, a2, az} will span R' unless h =

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Q: How many bijective functions have [10] as both the domain and codomain

A: Given, 10

Q: Let f and g be permutations on the set {1, 2, 3, 4, 5, 6, 7}, defined as follows (b) f 1 (c) fgf =…

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Q: The relation R on the set A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10) is defined by R= {(x,y) E AXA: xmod…

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Q: 12) The value of f, g,f,and g! are given in the table below live f (x) 3. -3 3 6 -2 -1 2. A) Eind h…

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Q: Suppose that f(2, 3,1) = 5, fz(2,3,1) = 2, fy(2,3,1) = 3 and f.(2, 3,1) = -1. %3D Then f(1.9, 3.3,…

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Q: K Match each function to its domain from the list below. Some domains may be used more than once,…

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Q: 3) Let f(x) = 1 + 3x on [-8, 2]. Find the number c that satisfies the mean value theorem. a) O C= b)…

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Q: 3) Compute A-1 using adjoint. -1 -2 -3 -41 1 2 3 Let A = 5 1 0 0

A:

Q: let G be the set of all triples of the form (k1, k2,1) or (k1,k2,-1), where the ki, i=1,2 are…

A: Given :  G = k1, k2, ±1 : k1, k2 ∈ℤ with the operation  k1, k2, 1l1, l2, -1 = k1+l2, k2+l1, -1 To…

Q: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} onto {1, 2, 3} (i

A: According to the question, To find the number of surjective (onto) functions from a set of size 10…

Q: (1) if is reflexive, symmetric, or transitive. For a, b = Z, define ab if a + b is a multiple of 3.…

A: A relation is a subset of the cartesian product A×B where A and B are non-empty sets. For cartesian…

Q: 1. List a pair of zero divisors of (M₂(Z), +, ×):

A: