Reasoning about implied relationships (e.g. paraphrastic, common sense, encyclopedic) between pairs of words is crucial for many cross-sentence inference problems. This paper proposes new methods for learning and using embeddings of word pairs that implicitly represent background knowledge about such relationships. Our pairwise embeddings are computed as a compositional function on word representations, which is learned by maximizing the pointwise mutual information (PMI) with the contexts in which the two words cooccur. We add these representations to the cross-sentence attention layer of existing inference models (e.g. BiDAF for QA, ESIM for NLI), instead of extending or replacing existing word embeddings. Experiments show a gain of 2.7% on the recently released SQuAD 2.0 and 1.3% on MultiNLI. Our representations also aid in better generalization with gains of around 6-7% on adversarial SQuAD datasets, and 8.8% on the adversarial entailment test set by Glockner et al. (2018).