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

A partial order P is defined on the set of natural numbers as follows. Here a/b denotes integer division. i)(0, 0) ∊ P. ii)(a, b) ∊ P if and only if a % 10 ≤ b % 10 and (a/10, b/10) ∊ P. Consider the following ordered pairs: i. (101, 22) ii. (22, 101) iii. (145, 265) iv. (0, 153) The ordered pairs of natural numbers are contained in P are ______ and ______ Correct Answer (101, 22) and (0, 153)

For ordered pair (a, b), to be in P, each digit in a starting from unit place must not be larger than the corresponding digit in b. This condition is satisfied by options (iii) (145, 265) => 5 ≤ 5, 4 < 6 and 1 < 2; (iv) (0, 153) => 0 < 3 and no need to examine further.

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