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Express the permutation (2 4 5)(1 3 5 5)(1 25) as a single cycle or as a product of cycles.

Express the permutation (2 4 5)(1 3 5 5)(1 25) as a single cycle or as a product of cycles.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question 5. (a) Express the permutation (2 4 5) (1 3 5 5)(1 2 5) 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 E R} consisting of points with rectangular coordinates (x, y), define the relation by (1.91) (2, 2) x1 = ₂. (c) Prove that is an equivalence relation on the set P. (d) Describe the equivalence classes geometrically.
Transcribed Image Text:Question 5. (a) Express the permutation (2 4 5) (1 3 5 5)(1 2 5) 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 E R} consisting of points with rectangular coordinates (x, y), define the relation by (1.91) (2, 2) x1 = ₂. (c) Prove that is an equivalence relation on the set P. (d) Describe the equivalence classes geometrically.
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