Let D30 = {1, 2, 3, 5, 6, 10, 15, 30} and relation I be a partial ordering on D30. The lub of 10 and 15 respectively is

 Let D30 = {1, 2, 3, 5, 6, 10, 15, 30} and relation I be a partial ordering on D30. The lub of 10 and 15 respectively is

A). 1

B). 5

C). 15

D). 30

Let D30 = $1, 2, 3, 5, 6, 10, 15, 30$ and relation I be a partial ordering on D30 defined by divisibility. The least upper bound (lub) of 10 and 15 is determined as follows:

1. Identify the elements in D30 that are greater than or equal to both 10 and 15 under the divisibility relation.
2. In a partial order defined by divisibility, $a \leq b$ means $a$ divides $b$.
3. The elements in D30 that are multiples of both 10 and 15 are: $ \text{lcm}(10,15) = 30 $
4. The least such element in D30 is 30, making it the least upper bound.

Thus, the least upper bound (lub) of 10 and 15 is:

$ \boxed{30} $

Answer: (D) 30.

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