## ABSTRACT

Let S and T be sets. A relation on S and T is a subset of S × T $S \times T$ https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9781315146898/9ce47cf6-5c02-4bc8-a80d-2160001f85a9/content/inline-math4_1.tif"/> . If R $\mathcal{R}$ https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9781315146898/9ce47cf6-5c02-4bc8-a80d-2160001f85a9/content/inline-math4_2.tif"/> is a relation, then we write either ( s , t ) ∈ R $(s,t) \in \mathcal{R}$ https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9781315146898/9ce47cf6-5c02-4bc8-a80d-2160001f85a9/content/inline-math4_3.tif"/> or sometimes s R t $s\, \mathcal{R}\, t$ https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9781315146898/9ce47cf6-5c02-4bc8-a80d-2160001f85a9/content/inline-math4_4.tif"/> to indicate that s is related to t or that (s, t) is an element of the relation. We will also write s ∼ t $s \sim t$ https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9781315146898/9ce47cf6-5c02-4bc8-a80d-2160001f85a9/content/inline-math4_5.tif"/> when the relation being discussed is understood.