Given: An array of size 'n'
Expected Output: Return (smallest element)
Finding the smallest value in a set of n elements is by definition imposing an order on that set. To return the smallest element in array, every element in the array needs to be traversed atleast once.
In any sorting technique, at least one pass is required to scan all the elements which would take \(\Omega\left(n\right)\) time at minimum. Any algorithm trying to read through all elements would take either n or greater than n time which would be \(\Omega\left(n\right)\)time. Even if you create a Tree of all the elements which would take at least \(\Omega\left(n\right)\) time and then you need traverse both left and right sub-trees in order to search for the minimum element. In effect, this means that you again need to traverse all elements to find the minimum.
\(T\left(n\right)\ =\ \Omega(n)\)