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 co-occur. 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 SQuAD2.0 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).