Relations may or may not have meaning associated with them. Two numbers are related by R if they are equal. We see that x S y if x and y have the same parity. The relationships expressed …

Important Question: Suppose property P is one of the properties listed in Section 1.5, and suppose R and S are relations on a set A, each having property P . Then the following …

8. Given the following relations on the set of real numbers, determine if they have any of the properties: sym-metric, antisymmetric, reflexive, irreflexive, and transitive.

Representing binary relations • We can represent a binary relation R by a table showing (marking) the ordered pairs of R.

If you learn to recognize partial orders or equivalence relations, you can get a lot of intuition for new concepts in a short amount of time. Why now? We’ll want relations over the next few …

R holds between x and y: many common relations (<, ≤, =, |, ≡) are expressed with the relational symbol in the middle.

A (binary) relation on A and B is a subset R A B. We often write aRb to mean (a; b) 2 R. The following are properties of relations on a set S (where above A = S and B = S are taken to be …