Question

1 multiple choice 1 point
is an upward drawing (hasse diagram) used to visually represent a partial order on a finite set?
yes
no, its for equivalence relations
only for relations that are symmetric
no, its only for infinite sets
2 multiple choice 1 point
a partial order must be reflexive, meaning every element is related to itself.
true
false
3 multiple choice 1 point
an equivalence relation partitions its domain into disjoint equivalence classes.
true
false

Explanation:

1. Question: Is an upward drawing (Hasse diagram) used to visually represent a partial order on a finite set?

A Hasse diagram is a graphical representation of a finite partially - ordered set. It uses upward - pointing lines to show the order relations between elements.

By the definition of a partial order relation \(R\) on a set \(A\), for all \(a\in A\), \((a,a)\in R\) (reflexive property).

An equivalence relation \(R\) on a set \(A\) satisfies three properties: reflexivity (\(aRa\) for all \(a\in A\)), symmetry (\(aRb\) implies \(bRa\)), and transitivity (\(aRb\) and \(bRc\) implies \(aRc\)). The equivalence classes \([a]=\{b\in A|aRb\}\) are non - empty, disjoint, and their union is \(A\).

Answer:

Yes

2. Question: A partial order must be reflexive, meaning every element is related to itself.