Proofs provide an argument for each answer Make it as proofl

Proofs: provide an argument for each answer. Make it as proof-like as you can.

a) For two regular languages L1 and L2, is L1L2 a proper subset of L1 always, sometimes, or never?

b) Prove or disprove (true or false): The regular expression (a+b)*c describes the language consisting of all words which end in \"c\".

Solution

a) Firstly if L1 and L2 are regular languages then L1L2 is also a regular language and it means concatenation.

So, L1L2 can never be a subset of L1.

b) Regular expression (a+b)*c denotes set of all words containing a and b and ending with c.