Use the substitution method to prove the merge sort algorithm is $\backslash ($ O$($n $\backslash$log n$)\backslash ).$

To help you define the recurrence relation you need for the substitution method, here's a summary of the number of operations involved with merge sort:

To use this algorithm to sort a set of $\backslash ($ n $\backslash )$ values, we:

$1.$ Use the algorithm twice, to sort two sets of $\backslash (\backslash$mathrm$\{$n$\}/2\backslash )$ values, then

$2.$ Merge the two sorted subsets in such a way that all $\backslash ($ n $\backslash )$ values are sorted. The number of operations required for this merge step is $\backslash ($ O$($n$)\backslash ).$

We used the substitution method in class to prove Big O for tail recursive Fibonacci and for recursive binary search. Show your work step$-$by$-$step