A tuple t ₁ of relation R subsumes tuple t ₂ of R, with respect to a query Q if for every database, tuple t ₁ derives all, and possibly more, answers to query Q than derived by tuple t ₂. Therefore, the subsumed tuple t ₂ can be ignored with respect to Q in the presence of tuple t ₁ in relation R. This property finds use in a large number of problems. For instance: during query optimization subsumed tuples can be ignored thereby avoiding the computation of redundant answers; the size of cached information in distributed and object oriented systems can be reduced by omitting subsumed tuples; constraints need not be checked and rules need not be recomputed when provably subsumed updates are made. We give algorithms for deciding efficiently when a tuple subsumes another tuple for queries that use arbitrary mathematical functions. We characterize queries for which, whenever a set of tuples T subsumes a tuple t then one of the tuples in T also subsumed t, yielding efficiently verifiable cases of subsumption.