Can anyone help with question?

Consider the following greedy algorithm for finding a shortest path from vertex s to vertex t in a given connected graph. 1) Initialize path P to s and set S to {s} 2) If s = t return P and exit 3) Find the edge (s,v) of minimum weight over all v S 4) Add the edge (s,v) to P and the vertex v to S 5) Set S v and go to step 2) Does this algorithm always find a shortest path from s to t? Either explain why it does or give a counterexample.