Find the parity of each permutation:
b) (1 2 3 4 5 6)(7 8 9)
c) (1 2 3 4 5 6)(1 2 3 4 5 7)
d) (1 2)(1 2 3)(4 5)(5 6 8)(1 7 9)
Please show steps. Thanks!
I do the first one you do the other ones.
Notice, $\displaystyle (123456) = (16)(15)(14)(13)(12)$ and $\displaystyle (789)=(79)(78)$.
Thus,
$\displaystyle (123456)(789) = (16)(15)(14)(13)(12)(79)(78)$.
Notice there are $\displaystyle 7$ transpositions, so it is an odd permutation.