Question 5 (Unit FA)10 marks lat X be the set of points in the plane with coordinates (m, n) where € (-1,0,1), shown bel

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Question 5 Unit Fa 10 Marks Lat X Be The Set Of Points In The Plane With Coordinates M N Where 1 0 1 Shown Bel 1 (36.26 KiB) Viewed 43 times

Question 5 (Unit FA)10 marks lat X be the set of points in the plane with coordinates (m, n) where € (-1,0,1), shown below. The symmetry group of the figure comprising the set X is S(O), whose nos-identity elements are shown below. 1 An action of S(O) on the wet X is defined in the natural way, that is by DAPP for all y S(O) and all PEX (This is a group action by Theorem ESO.) (a) Write down the orbit and the stabiliser of each of the following points under this ston, wrifying in rach cwe that your stuwers satisfy the pustion in the Orbit Stabiliser Theoret, (1) 00) (6) Explain bow know that in (a) we found all the ots of 11 12 c) Write down the band touch of the elements and roo)