On the optimality of some set and vector algorithms

Optimality, to within a multiplicative constant, is shown for some algorithms dealing with vectors and finite sets. Among the problems discussed are: Is vector x equal to vector y ? Given two finite sets A and B, is A = B ? Is A ⊆ B ? Is A ∩ B = φ ? What is |A ∩ B| ? What is |A - B| ? Is A - B = φ ?