Given Language L = { a^n b^m } where n is even and m is even
In simple words we can consider this Language as even no of a's followed by even no of b's .If we write down the Language then it would be something like this....
L = {∈ , aa , bb , aaaa , bbbb ........}
Option 1 Grammar can't give us "aa" as a substring so it is not the correct option.
Option 3 Grammar can't give us "bb" as a substring so it is not the correct option.
It seems like option 2 can give us even no of a's followed by even no of b's but it is not true because initially we can get even no of a's then off-course we can even get even no of b's but there is a small problem in it that is the production "S1 --->bSb " due to this production we can get even no of a's in middle of b's and it should not be happened. So it is not the correct option.
Option 4 can give us exactly what we want out of given Grammar and 'll satisfy the Given Languge.