As you can imagine, the cryptic nature of how we describe TMs¹ make it easy to define one incorrectly. It is one thing if a set of rules doesn't produce the desired result. In such a case, ITM will simply follow the rules to an incorrect conclusion. There are, though, ways to define a TM so that it confuses or simply terminates the simulator. Let's examine three of them here. For each exercise, write down the TM that you define, run it in ITM, and answer the question posed. Your machines need not address any "real" problem other than that of illustrating the situation described.

1. Define a TM that demonstrates what happens when ITM runs a TM that contains ambiguous rules (that is, more than one rule for a given input symbol-state pair)?
   
   
2. Define a TM that demonstrates what happens when ITM runs a TM which directs it to move off the left edge of the tape?
   
   
3. Define a TM that demonstrates what happens when ITM runs a TM with an incomplete rule base (for example, the rules of the TM direct the simulator to a particular state, and there are no rules describing what it should do in that state).