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.

• There are three taps A, B and C in a tank. They can fill the tank in 25 hrs, 20 hrs and 10 hrs respectively. At first all of them are opened simultaneously. Then after 1 hrs, tap C is closed and tap A and B are kept running. After the 4th hour, tap B is a
• A and B can complete a piece of work in 80 and 120 days respectively. They together start the work but A left after 20 days. After another 12 days C joined B and now they complete the work in 28 more days. In how many days C can complete the work, working
• S, T and U can complete a work in 40, 48 and 60 days respectively. They received Rs 10800 to complete the work. They begin the work together but T left 2 days before the completion of the work and U left 5 days before the completion of the work. S has com
• The letters A, B, C, D, E, F and G not necessarily in that order, stand for seven consecutive integers from 1 to 10, D is 3 less than A, B is the middle term. F is as much less than B as C is greater than D, G is greater than F.
• Two vessels contain mixtures of milk and water in the ratio of 8 : 1 and 1 : 5 respectively. The content of both of these are mixed in a specific ratio into a third vessel. How much mixture must be drawn from the second vessel to fill the third vessel (ca

B I U OL Table

Captcha

Refresh

Submit Answer