doubt

Question

L ⊆ Ʃ*, Ʃ = {a, b} Which of the following is True?
(a) L = {x | x has equal a’s and b’s} is regular
(b) L = {a^n b^n | n ≥ 1} is regular
(c) L = {x | x has more a’s than b’s} is regular
(d) L = { a^m b^n, m,n ≥ 1} is regular

Comments

only option d is true ?

Answer 1

a) is wrong as here no of a's and b's are equal which needs comparison and counting and thus a aDFA cant be drwan for it..

b) is wrong due to the above reason.

c)wrong , here no of a's > no of b's thus again counting and comparison is required and drawing dfa is not possible as dfa has finite memory.

d)is true and  is regular language.

Answer 2

               d) is correct answer :)
 

reg exp :a⁺b⁺