We define two lifted, total relation semantics for Event B machines: Safe B for safety-only properties and Live B for liveness properties. The usual Event B proof obligations, Safe, are sufficient to establish Safe B refinement. Satisfying Safe plus a simple additional proof obligation ACT REF is sufficient to establish Live B refinement. The use of lifted, total relations both prevents the ambiguity of the unlifted relational semantics and prevents operations being clairvoyant.