Please help with the following questions:

Q1.4 4 Points = Consider a connected undirected graph G (V, E) with nonnegative edge weights w. Now suppose each edge weight is increased by 1: w'(u, v) = w(u, v) + 1 for each (u, v) E E. Claim: If P is a shortest path of G between vertex x and vertex y with respect to edge weights w, then P must also be a shortest path of G between vertex x and vertex y with respect to edge weights w'. O True O False Q1.5 4 Points Consider a connected undirected graph G = (V, E) with nonnegative edge weights w. Now suppose each edge weight is increased by 1: w'(u, v) = w(u, v) + 1 for each (u, v) E E. Claim: If T is a minimum spanning tree of G with respect to edge weights W, then it must also be a minimum spanning tree of G with respect to edge weights w'. True O False