Theory of Automata Assignment #1 Part #3 Recursive Definition #11: Language of Expressions having at least one operator defined on Σ ={+,-,*,/,a,b} Step 1#- a+b ,a*b,a/b and a-b are in L Step 2#- If x is in L then x+x,x-x,x*x,x/x is also in L Step 3#- No words except generated above can be considered as member of Language. Recursive Definition #12: Language of string starting and ending on different alphabet defined on Σ ={a,b} Step 1#- ab and ba are in L Step 2#- If x is in L then axb,and bxa are also in Σ*. Step 3#- No words except generated above can be considered as member of Language. Recursive Definition #13: Language of even numbers Step 1#- 0 and 2 are in L Step 2#- If x is in L then x+2 and x-2 is also in L . Step 3#- No words except generated above can be considered as member of Language. Recursive Definition #14: Language of negative integers defined on Σ ={-1,-2,-3,-4,-5,-6,-7,-8,-9} Step 1#- -1 and -2 are i