3. Let w be a string of symbols and let the language T be defined as adding w to the language S, i.e., T-SUlw). Suppose further that T-S (a) Is it necessarily true that w E S? If this is necessarily true, give a proof. If this is not necessarily true, give a counterexample. (b) Is it necessarily true that w ES*? If this is necessarily true, give a proof. If this is not necessarily true, give a counterexample