The traditional = operator is an equivalence relation

Reflexive: Yes a=a

Symmetric: Yes if a=b, then we know b=a

Transitive: Yes if a=b and b=c, then we know a=c

Partial order is a set where some elements are less than others but others are not.

The <= operator is a partial ordering.

Also, a class schedule with prerequisites is partially ordered. You need to take CS53 and Math103 before you take Stat232 but you can take CS53 and Math103 in any order.

So CS53 precedes Stat232 and Math103 precedes Stat232, but we can't say CS53 or Math103 precedes the other.

Reflexive: Yes a=a

Symmetric: Yes if a=b, then we know b=a

Transitive: Yes if a=b and b=c, then we know a=c

Partial order is a set where some elements are less than others but others are not.

The <= operator is a partial ordering.

Also, a class schedule with prerequisites is partially ordered. You need to take CS53 and Math103 before you take Stat232 but you can take CS53 and Math103 in any order.

So CS53 precedes Stat232 and Math103 precedes Stat232, but we can't say CS53 or Math103 precedes the other.