Answer
All three sorted lists are $\{1,2,3,4,5\}$. Check the solution for an explanation of how the selection sort worked.
Work Step by Step
The selection sort is characterized by doing the following for each iteration $i$:
It selects the smallest value and inserts it at the $i^{th}$ location by swapping it whatever value is at that location.
a) We begin with the set $\{3,5,4,1,2\}$
For the first iteration, the algorithm loops over the entire set and decides that $1$ is the least element. It is swapped with the element in that location giving us $\{1,5,4,3,2\}$
For the second iteration, the algorithm loops over the entire set and decides that $2$ is the least element. It is swapped with the element in that location giving us $\{1,2,4,3,5\}$
For the third iteration, the algorithm loops over the entire set and decides that $3$ is the least element. It is swapped with the element in that location giving us $\{1,2,3,4,5\}$
For the final iteration, the smallest value is at the appropriate location and hence no changes are made.
b) We begin with the set $\{5,4,3,2,1\}$
For the first iteration, the algorithm loops over the entire set and decides that $1$ is the least element. It is swapped with the element in that location giving us $\{1,4,3,2,5\}$
For the second iteration, the algorithm loops over the entire set and decides that $2$ is the least element. It is swapped with the element in that location giving us $\{1,2,3,4,5\}$
For the third and fourth iteration, the smallest value is at the appropriate location and hence no changes are made.
c) b) We begin with the set $\{1,2,3,4,5\}$
For every iteration of the algorithm, the smallest value is at the appropriate location and hence no changes are made.
