Original question was with simply < condition. (Please correct the questions)
(a, b) ∊ P if and only if a % 10 < b % 10 and (a/10, b/10) ∊ P
(i) (101,22) is in P :
Reason: 101%10 < 22 %10 implies 1 < 2 is true
and (101/10, 22/10) = (10,2) should be in P, So we should verify (10,2) pair : (10%10 < 2%10) implies 0 < 2 is true and (10/10, 2/10) = (1,2) is in P. So pair (101, 22) is in P
(ii) (22, 101) is not in P:
22%10 < 101%10 implies 2 < 1 is false. Therefore (ii) is not in P.
(iii) (145, 265) is not in P:
145 %10 < 265 %10 implies 5 < 5 is false. Therefore (iii) is not in P.
(iv) (0, 153) is in P :
Reason: 0%10 < 153 %10 implies 0 < 3 is true
and (0/10, 153/10) = (0, 15) should be in P, So we should verify (0,15) pair: (0%10 < 15%10) implies 0 < 5 is true and (0/10, 15/10) = (0,1) is in P.
So pair (0, 153) is in P
Answer is (i) and (iv) : Option (C) is correct.