Finite / Infinite Languages True/False and why? Just doing some work on Finite and infinite languages. And came across some statements I know the answer to but not sure how to explain why. 


There are finitely many finite languages. 
-This is false right? Since there are technically infinitely many finite languages
Union of any two languages over alphabet (1,0) is regular. 
-False right? Since you can take a (non-reg U non-reg = non-reg)
Single state NFA can recognize only finite languages
-False, but I have no idea how to explain why...
False. There are infinitely many finite language. Just think of {0,1}*. This is a infinite set of finitely long strings. or say, it is union of infinite number of finite languages over {0,1} which have strings of finite length.
False. Union of two non regular languages MAY BE regular but it not the case always. This answer explains it well.
False. Lets have a single state NFA having state q0. let 'd' be the transition function. d(q0, a) = q0 and since this is single state NFA, q0 is also final state.
This NFA will accept all strings having only 'a'. i.e. {a,aa,aaa,aaaa...} The cardinality of this set is infinite, hence it can accept infinite languages too.