Relations -Basic Notations the identity on S Ids {(x,x)|x∈S) the domain of p dom(p) f{x1y.(x,y)∈p} the range of p ran(p)de fyx(x,y)ep} composition of p and p pop e {(x,z）I3y.(x,y)∈pA(y,z)∈p} inverse of p p-1 {(y,x)I (x,y)Ep} 13/40Relations – Basic Notations the identity on S IdS def = {(x, x) | x ∈ S} the domain of ρ dom(ρ) def = {x | ∃y.(x, y) ∈ ρ} the range of ρ ran(ρ) def = {y | ∃x.(x, y) ∈ ρ} composition of ρ and ρ 0 ρ 0 ◦ ρ def = {(x, z) | ∃y.(x, y) ∈ ρ ∧ (y, z) ∈ ρ 0} inverse of ρ ρ−1 def = {(y, x) | (x, y) ∈ ρ} 13 / 40