Question

Даны языки L1={a,aa,abb,bab,baab,bbab,babca}, L2={bab,ab,abba,babca} Показать чему будет равны результаты конкатенации, дизъюнкции, конъюнкции, разности для этих языков

Answer 1

$L_1L_2=\{aaab,\:aaabba,\:aab,\:aabab,\:aababca,\:aabba,\:abab,\:ababca,\:abbab,\:abbabba,\\ \:abbbab,\:abbbabca,\:baabab,\:baababba,\:baabbab,\:baabbabca,\:babab,\:bababba,\\ \:babbab,\:babbabca,\:babcaab,\:babcaabba,\:babcabab,\:babcababca,\:bbabab,\:bbababba,\\ \:bbabbab,\:bbabbabca\}$$L_2L_1=\{aba,\:abaa,\:ababb,\:abbaa,\:abbaaa,\:abbaab,\:abbaabb,\:abbab,\:abbabaab,\\ \:abbabab,\:abbababca,\:abbabbab,\:abbabca,\:abbbab,\:baba,\:babaa,\:bababb,\:babbaab,\\ \:babbab,\:babbabca,\:babbbab,\:babcaa,\:babcaaa,\:babcaabb,\:babcabaab,\:babcabab,\\ \:babcababca,\:babcabbab\}$

$L_1\cup L_2=L_2\cup L_1=\{a,aa,abb,bab,baab,bbab,babca,ab,abba\}$

$L_1\cap L_2=L_2\cap L_1=\{bab, babca \}$

$L_1\backslash L_2=\{a,aa,abb,baab,bbab\}$

$L_2\backslash L_1=\{ab,abba\}$