It is important to to know that
(i) We are not dividing the number with 7 but we are observing if the number is divisible by 7.
(ii) It should start with 1.
For part (i):
So,we can see for divisibility by 7 by counting the remainders as
(1) Remainder 0
(1) Remainder 1
(2) Remainder 2
(3) Remainder 3
(4) Remainder 4
(5) Remainder 5
(6) Remainder 6
So, 7 states are sufficient to check divisibility by 7.So, its regular.
Its regular because its starts with 1.And for 0 we reject it.
Thus , part (i) and part (ii) both are regular.And due to closure property the entire statement is regular.Option A is correct