Proof:
Theorem: The family of regular languages is
closed under union, concatenation, iteration.
Closure properties 2/2
• Let L1, L2 be two regular languages
• Then, there exist two REs r1, r2: L(r1) = L1, L(r2) = L2;
• By the definition of regular expressions:
• r1.r2 is a RE denoting L1 L2
• r1 + r2 is a RE denoting L1 È  L2
• r1* is a RE denoting L1*
• Every RE denotes regular language, so
 L1 L2,  L1 È  L2,  L1* are a regular languages
14/26