###### 1.

Express $$(1\,3\,4)(3\,5\,4)$$ as a cycle, or a product of disjoint cycles. (Interpret the composition of functions in the order used by Sage, which is the reverse of the order used in the book.)

###### 2.

What is a transposition?

###### 3.

What does it mean for a permutation to be even or odd?

###### 4.

Describe another group that is fundamentally the same as $$A_3\text{.}$$

###### 5.

Write the elements of the symmetry group of a pentagon using permutations in cycle notation. Do this exercise by hand, and without the assistance of Sage.