Discrete Mathematical Structures, Lecture 4.1: Binary relations on a set

Discrete Mathematical Structures, Lecture 4.1: Binary relations on a set.

A binary relation R on a set S is any subset of SxS. An element of R, written (a,b), or sometimes aRb, means that "a is related to b". Two important special cases are equivalence relations, which in some sense generalizes "equality", and partial orders, which in some sense generalize "less than or equal to". An equivalence relation is any
relation that is reflexive (every element is related to itself), symmetric, and transitive. A partial order is any relation that is reflexive, symmetric, and antisymmetric. In this lecture, we give a number of motivation examples of binary relations, and discuss which ones are equivalence relations, which are partial orders, and which are neither.

[jenyaz]

The length is fine, thank you for sharing these

[mohammedal-haddad]

These lectures are great, but they are rather long. I'd prefer lectures that last 10-15 minutes. However, I really appreciate this nice explanation.