Draw the hasse diagram representing the partial ordering

sairam polapally

sairam polapally

Answered question

2022-07-07

Draw the hasse diagram representing the partial ordering {(a,b)|ab}.

Answer & Explanation

alenahelenash

alenahelenash

Expert2023-06-18Added 556 answers

To draw the Hasse diagram representing the partial ordering {(a,b)ab}, we first need to understand the elements involved and the ordering relationship.
In this case, the partial ordering is defined as follows: for elements a and b, (a,b) is in the relation if and only if a is less than or equal to b.
Now, let's create the Hasse diagram:
1. Start by representing all the elements of the set as nodes in the diagram. In this case, the elements are a and b.
2. Draw a directed edge (line) from a to b if and only if a is less than or equal to b.
Since there are only two elements, a and b, and the ordering relation is defined as , we can construct a simple Hasse diagram with two nodes and a single directed edge from a to b:
a -> b
In this diagram, a is positioned below b to indicate that a is less than b. The directed edge represents the ordering relation.
This completes the construction of the Hasse diagram representing the given partial ordering {(a,b)ab}.

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