Binary relations, such as equality, are basic mathematical concepts that appear, implicitly or explicitly, in most benchmarks for Large Language Models (LLM). A recent trend in the literature is benchmarking LLMs on out-of-context learning, where the data is not presented in the prompt, but only during the model's training. However, existing works mostly focus on higher-order tasks, making it hard to interpret success or failure. In this work, we study how well can LLMs reason out-of-context on binary relations by only learning the representations of newly introduced tokens. Our experiments focus on equality (=), inequality (<), and inclusion (subset) and the properties they satisfy, such as reflexivity, symmetry, transitivity, and logical complexity (e.g., the number of reasoning "hops"). We show that LLMs achieve better than random accuracy, but are still far from perfect, even on relatively simple reasoning tasks involving binary relations. We analyse the learned representations and show that LLMs encode useful information directly, arranging the embeddings according to the task.