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-p.s3.eu-west-1.amazonaws.com/9781315146898/a1b9795b-e4b0-4fee-8c32-bca69881dde3/content/inline-math4_1.tif"/> . If R $ \mathcal{R} $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315146898/a1b9795b-e4b0-4fee-8c32-bca69881dde3/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-p.s3.eu-west-1.amazonaws.com/9781315146898/a1b9795b-e4b0-4fee-8c32-bca69881dde3/content/inline-math4_3.tif"/> or sometimes s R t $ s\, \mathcal{R}\, t $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315146898/a1b9795b-e4b0-4fee-8c32-bca69881dde3/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-p.s3.eu-west-1.amazonaws.com/9781315146898/a1b9795b-e4b0-4fee-8c32-bca69881dde3/content/inline-math4_5.tif"/> when the relation being discussed is understood.
