Question  1:  Find a minimal spanning tree for the connected weighted graph using
(i) Kruskal's method
(ii) Prim's Method

Question  2: Apply Dijkastra's algorithm to find shortest path from the vertex s to vertex t.
 

Question 3: A committee is to selected from five candidates a, b, c, d and e. The selection must satisfy all the following conditions.

(i) Either a or b must be included but not both.
(ii) Either c or e both must be included.
(iii) If d is included, then b must be included.
(iv) Either both a and c are included or neither is included.
(v) If e is included, then c and d must be included.

How should the selection be made?

 Question 4 : Enumerate various steps, which can be useful in translating statements or arguments in English to corresponding statements or arguments in formal language like Propositional Calculus or First Order Predicate calculus (FOPC). Further translate the following arguments in English to corresponding arguments in a Formal Language (only PC/FOPC) and check in PC/FOPC the validity of argument: