For the following statements indicate whether it is true or

For the following statements, indicate whether it is true or false, and provide justification for your answer (not a formal proof, just a justification). If your answer is false provide a counterexample. The class of infinite languages is closed under complementation. The class of infinite languages is closed under concatenation. The class of infinite languages is closed under intersection.

Solution

1.FALSE:

If L is an infinite language, then -L need not be an infinite language.

2. TRUE :

If L1 and L2 are two infinite languages, then L1L2 is also infinite language.

3.FALSE:

  If L1 and L2 are two infinite languages, then L1 L 2 need not neccesarily be infinite language.