Def: Let w be a set of ordered pairs. The inverse of w is defined by:
w-1 = { (y,x) | (x,y)∈w }
Def: Let w be a set of ordered pairs and p be any set. The restriction of w on p is defined by:
restrict(w,p) = { (x,y)∈w | x∈p }
Def: Let f and g be sets of ordered pairs. The composition f∘g is defined by:
f∘g = { (x,z) | (x,y)∈g ∧ (y,z)∈f }
Def: Let w be a set of ordered pairs. The domain and image of w are defined by:
dom(w) = { x | (x,y) ∈ w }
image(w) = { y | (x,y) ∈ w }