partial order

Question

A partial order P is defined on the set of natural numbers as follows. Here x/y denotes integer division.
i. (0, 0) ε P.
ii. (a, b) ε P if and only if a % 10 ≤ b % 10 and (a/10, b/10) ε P.
Consider the following ordered pairs:
i. (101, 22)
ii. (22, 101)
iii. (145, 265)
iv. (0, 153)
Which of these ordered pairs of natural numbers are contained in P?
A) (i) and (iii)
B) (ii) and (iv)
C) (i) and (iv)
D) (iii) and (iv)

I am getting (i) is also correct because 101%10=1,22%10=2 so 1<2 and 101/10=10 and 22/10=2 so 10%10=0 and 2%10=2 which is 0<2 so answer (i) should be correct.

Answer 1

answer should be (i) and (iii) that is A. (ii) is not following the criteria of a%10<=b%10.. and about (iv) since P is only defined on the set of natural number.. and 0 is not a natural number that's why A. Am i correct?

Comments

but answer given in gateoverflow book is d ,thats why i am asking question ,(iv) is also correct because you see (0,0) belongs to p.