By a, b, f, r, the following permutations of the set {1,2,3,4,5,6} are given.
a) Determine the unknown permutations g and h if the equations
for g ◦ h = r and h◦a = b apply.
b) Find (f ◦g◦h)2 = (f ◦g◦h) ◦ (f ◦g◦h).
By a, b, f, r, the following permutations of the set {1,2,3,4,5,6} are given. a) Determine the u...
(1 point) Let f and g be permutations on the set {1, 2, 3, 4, 5, 6, 7}, defined as follows (1 2 3 4 5 6 7 JE (3 1 6 5 7 2 4) f = (1 800 2 5 3 4 4 7 5 3 6 2 7 6) Write each of the following permutations as a product of disjoint cycles, separated by commas (e.g. (1,2), (3,4,5), ... ). Do not include 1-cycles (e.g. (2)) in your...
Solve for 1 Consider the following permutations f, g, and h in S6 - (1 2 3 4 5 6) (1 2 3 4 5 6 16 1 3 5 4 2 8 2 3 1 6 5 4) 1 /1 2 3 4 5 6 na 3 1 6 4 5 2 / 5 g gº g=
abstract-algebra Problem 10.2. Consider the following permutations f and g in the permutation group 56: f:145, 241, 366,44 3,5 H 2,6 H4; g=(1 6 5)( 24). (1) Write f as a product of disjoint cycles. (2) Find o(g). (3) Write fg as a product of disjoint cycles. (4) Write gf as a product of disjoint cycles. (5) Write gfg as a product of disjoint cycles. Hint. All should be straightforward. Be careful though.
a = 14. Consider the permutations (13)(24)(56) and B = (1 4)(26)(35) expressed in cycle notation. How many permutations y of {1,2,3,4,5,6} exist with the property B = y lay where we compose from left to right? (b) 48 (c) 6 (d) 24 (e) 3 (a) 8 1 15. You are given that {a,b,c} = {1,2,3} and, from the 8-puzzle 2 3 4 5 6 7 8 the following configuration has been reached by moving squares in and out of...
a. e. b. f. 7. Given the function f(x) = 4(2)* - 3 , the equation of the horizontal asymptote is a. X=-3 e. y=-3 b. X=4 f. y = -2 c. X= 3 g y = 2 d. y = 0 h. none of these 8. If we apply the mapping (x,y) → (x-3,- 2y + 1) to f(x) = (3)* , the equation of the image is y = 2(3) *-3 + 1 y=-(3)*+2 + 1 =-2(3)*+3+1 y=-2(3)*+3...
Q3: Given a relational schema R = {A,B,C,D,E,F,G,H,1,J,K} and a set of functional dependencies F {A B C D E, E F G H I J,AI →K} and a key(R) = AI = 1. Is R in BCNF? If yes, justify your answer [5 points] 2. If no, explain why and decompose R for two levels only [10 points] 3. Check whether the decomposition in step 2 dependency preserved or not [5 points]
1. Given the data table with f(x) = yn for a unkown function f, determine the cubic spline interpolation that intersects with the 3 data points. No need to solve for the coefficients. Just set up the eight equations. 1.1 3.5 1.2 3.7 1.3 2.9 2. The fixed point iteration can be used to find the solution of a function f(r) = 0. To use this method, we need to first identify g(x) such that the solution of g(x) =...
Set theory Find f(A) and f-(B) for the given function and sets. (a) f : R → R is defined by f(x) = x2 + 1, A = [-1,2], B = [0,4]. (b) f R R is defined by f(x) - sin z, A [0, ], B [0,2]. (c) f : R → Z is defined by f(x)-번 (the floor function), A = (0,4], B-(0,1,2). (d) f : R-(0) → R is defined by f(z) = x + 1, As...
(2) Consider the function f given by f:R R f(a)1 2 (a) Determine the domain D and range R of the function f. (b) Show that f is not one to one on D. (c) Let ç D be a subset of the domain of f such that for all x ? S, 0 and the function is one to one. Find such a set S. (d) For the set S given in Part (c), find f (x) (e) Determine...
11. Let the universal set be the set U = {a,b,c,d,e,f,g} and let A = {a,c,e,g} and B = {d, e, f, g}. Find: A ∪ B 12. Let the universal set be the set U = {a,b,c,d,e,f,g} and let A = {a,c,e,g} and B = {d, e, f, g}. Find: b. A ∩ B 13. Let the universal set be the set U = {a,b,c,d,e,f,g} and let A = {a,c,e,g} and B = {d, e, f, g}. Find: AC...