(a) Express the permutation (2 4 5)(1 3 5 5)(1 2 5) as a single cycle or a s a product of cycles.(b) How many elements of the permutation group Se map 2 to 2 and 5 to 5, while the re-maining numbers in the set S = {1, 2, 3, 4, 5, 6} are free to permute?In the Cartesian plane P = {(x,y): x, y ≤ R} consisting of points with rectangularcoordinates (x, y), define the relation by (x1, y₁) (x2, Y2)x1 = x₂.(c) Prove that ~is an equivalence relation on the set P.(d) Describe the equivalence classes geometrically.

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(a) Express the permutation (2 4 5)(1 3 5 5)(1 25) as a single cycle or as a product of cycles. (b) How many elements of the permutation group Se map 2 to 2 and 5 to 5, while the re- maining numbers in the set S = {1, 2, 3, 4, 5, 6} are free to permute? In the Cartesian plane = {(x, y): x, y ≤ R} consisting of points with rectangular coordinates (x, y), define the relation~ by (x1, y1)~ (x2, Y2) x1 = x₂. (c) Prove that ~ is an equivalence relation on the set P. (d) Describe the equivalence classes geometrically.

(a) Express the permutation (2 4 5)(1 3 5 5)(1 25) as a single cycle or as a product of cycles. (b) How many elements of the permutation group Se map 2 to 2 and 5 to 5, while the re- maining numbers in the set S = {1, 2, 3, 4, 5, 6} are free to permute? In the Cartesian plane = {(x, y): x, y ≤ R} consisting of points with rectangular coordinates (x, y), define the relation~ by (x1, y1)~ (x2, Y2) x1 = x₂. (c) Prove that ~ is an equivalence relation on the set P. (d) Describe the equivalence classes geometrically.

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter12: Angle Relationships And Transformations

Section12.6: Rotations And Symmetry

Problem 1C

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