a$.$ If the program syntax is faulty, then the computer will generate an error message.

If the computer generates an error message, then the program will not run.

Therefore, if the program syntax is faulty, then the program will not run.

b$.$ If this simple graph, then it is complete. If this graph then any two of its vertices can be joined by a path.

Therefore, if this simple graph has $4$ vertices and $6$ edges, then