On Knights and Knaves Island, all natives are either knights, who always tell the truth, or knaves, who always tell lies

1. On Knights and Knaves Island, all natives are either knights, who always tell the truth, or knaves, who always tell lies.

You meet 3 natives:  A, B and C.

A says “B and C are of the same type”.

C says “B is a knave”.

1. Use calculational logic to determine whether A is a knight or a knave.

Show your working. (5 Marks)

1. Can you tell if B is a knight or a knave? Explain your answer. (5 Marks)

1. Parts a. to e. all refer to the following graph.

1. Is this graph weighted? (2 Marks)
2. Is this graph complete? (2 Marks)
3. Is this graph acyclic? (2 Marks)
4. Is this graph directed? (1 Mark)
5. Construct a minimal spanning tree using the node-at-a-time algorithm, starting at node A. Specify each added edge, in the order they are added by specifying the pair of nodes it joins (e.g. A-D). (3 Marks)