Relations We need to first define the Cartesian product of two sets A and B: A×B={(x,y)Ix∈A and y∈B} Here (x,y)is called a pair. Projections over pairs: πo(x,y）=xand1(x,y)=y. Then.p is a relation from A to B if pC Ax B,or pEP(Ax B) 11/40Relations We need to first define the Cartesian product of two sets A and B: A × B = {(x, y) | x ∈ A and y ∈ B} Here (x, y) is called a pair. Projections over pairs: π0(x, y) = x and π1(x, y) = y. Then, ρ is a relation from A to B if ρ ⊆ A × B, or ρ ∈ P(A × B). 11 / 40