Q 34,. paper3,j12.Consider a weighted undirected graph with positive edge weights and let (u, v) be an edge in the graph. It is known that the shortest path from source vertex s to u has weight 53 and shortest path from s to v has weight 65. Which statement is always true ?

Options (A) Weight (u, v) <12
(B) Weight (u, v) = 12
(C) Weight (u, v) >=12
(D) Weight (u, v) > 12
Anwer© Weight (u, v) >=12.
Explanation. We know weight(S,U)=53 and weight (S,V)=65 then weight (u,v) will be greater than 12 because sum of two sides of a triangle is greater than or equal to the third side.(Triangle inequality).