Trivial relation


Definition

$$\forall x,y \in S : x{\mathrel{R}}y$$
LEMMA   

The trivial relation is reflexive.

Proof available

LEMMA   

The trivial relation is symmetric.

Proof available

LEMMA   

The trivial relation is transitive.

Proof available

THEOREM   

The trivial relation is an equivalence relation.

Proof available

Proper supersets