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

Ans. 1. False: Every infinite language has a finite language as its complement.
Ans. 2. True
Ans. 3. True