Question: Problem 13. Let X = {1,2,3,4} and let A = {1,2} and B = {3,4}. Let G be the set of all bijections : X

Problem 13. Let X = {1,2,3,4} and let A = {1,2} and B = {3,4}. Let G be the set of all bijections : X X having the property that either (A) = A or (A) = B. (Here a mapping applied to a subset of X means the subset of images: (U) ={(u) : uU}. WritedowntheelementsofG andlabelthemsomehow. Thenwritetheoperationtable(Cayley table) for operation of composition on G. Is G commutative?

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