Union of two languages Let E$=\{$a$,$b$\}.$

Let L$1=\{$starts with a and ends with b$\},$ L$2=\{$starts with b and ends with a$\}.$ Draw the DFA for L$1,$ L$2,$ and L$1$UL$2.$

Intersection of two languages

Let E$=\{0,1\}.$ Let L$1=\{$set of all binary strings ending in $01\},$ L$2=\{$set of all binary strings with even number of $1$s$\}.$ Draw the DFA for L$1,$ L$2,$ and L$1$ L$2.$

Difference of two languages:

Let E$=\{0,1\}$

Design a DFA which accepts all strings that does not contain the string $00$ but ends wiht $01.$

Design a DFA which accepts all string that contains the string $00$ but does not end with $01.$