Drawing inferences between open-domain natural language predicates is a necessity for true language understanding. There has been much progress in unsupervised learning of entailment graphs for this purpose. We make three contributions: (1) we reinterpret the Distributional Inclusion Hypothesis to model entailment between predicates of different valencies, like DEFEAT(Biden, Trump) entails WIN(Biden); (2) we actualize this theory by learning unsupervised Multivalent Entailment Graphs of open-domain predicates; and (3) we demonstrate the capabilities of these graphs on a novel question answering task. We show that directional entailment is more helpful for inference than bidirectional similarity on questions of fine-grained semantics. We also show that drawing on evidence across valencies answers more questions than by using only the same valency evidence.