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Union of two regular languages
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Union of two regular languages : ウィキペディア英語版
Union of two regular languages

In formal language theory, and in particular the theory of nondeterministic finite automata, it is known that the union of two regular languages is a regular language. This article provides a proof of that statement.
==Theorem==

For any regular languages L_ and L_, language L_\cup L_ is regular.''
''Proof''
Since L_ and L_ are regular, there exist NFAs N_,\ N_ that recognize L_ and L_.
Let
:: N_ = (Q_,\ \Sigma ,\ T_,\ q_,\ A_)
:: N_ = (Q_,\ \Sigma ,\ T_,\ q_,\ A_)

Construct
::N = (Q,\ \Sigma ,\ T,\ q_,\ A_\cup A_)

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