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.

Part (ii)

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