In this paper we investigate the relevance logic E-R of the Entailment E without the reductio (R), and its extensions Ee-R, Eec-R: Ee-R is the E-R with the expansion (e) and Eec-R the Ee-R with the chain (c). We give completeness for each E-R, Ee-R, and Eec-R by using Routley-Meyer semantics.