be a fixed element
of Sn.
Show that f : Sn -> Sn defined by
f(
) =
-1,
for all in Sn,
is a one-to-one and onto function.
= (1,3,5,7,9),
= (1,2,6), and
= (1,2,5,3).
For =
,
write as a product of disjoint cycles,
and use this to find its order and its inverse. Is
even or odd?
2. Define the function f : Z17× -> Z17× by f(x) = x-1, for all x in Z17×. Is f one to one? Is f onto? If possible, find the inverse function f-1.
3.
(a) Let be a fixed element
of Sn.
Show that f : Sn -> Sn defined by
f() =
-1,
for all in Sn,
is a one-to-one and onto function.
(b) In S3, let
= (1,2).
Compute the corresponding function f defined in part (a).