I am new to ArcGIS Pro and trying to learn how to do analysis with rasters. I have two raster datasets: one with an elevation profile of a US state, and another showing land use. I am trying to create a new raster that shows an intersection between land use of a specific category and elevation <1000. In ArcGIS Pro, what tool should I use to create the new raster?

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You want to use the Con (Conditional) tool, either standalone or within the Raster Calculator to put together a statement roughly like Con(elevation<1000 AND landuse==X, true_output, false output). There are a handful of different ways you can phrase the same query depending on which tool you use, so treat my syntax with a grain of salt. This Esri blog post gives a far more in depth answer on how to use a complex statement within the Con tool for a very similar kind of habitat/suitability question.

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