GATE | Gate IT 2007 | Question 23

A partial order P is defined on the set of natural numbers as follows. Here x/y 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)

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)

Answer: (D)


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