# Set math

Takes as input two (or more) object sets *of the same type* and returns a combined object set based on operations defined by the user. Supported operations are the union, intersection, or difference of two object sets.

## Input type

Object set

## Output type

Object set

## Examples

In the example below, we are using set math to find the difference between a set of 48,895 Airbnb objects (`$B`) and a filtered set of 22,326 Airbnb objects (`$D`). The output is the set (`$E`) of 26,569 Airbnb objects in `$B` but not in `$D`.

Airbnb data used in this example is open source.

![Example of set math](../../../assets/26f4992cb7a5f1c27e52006ecb2a8fc30e9aa41db92df4129bb744941212d6f8.webp)

## Usage information

| Functionality | Availability |
| --- | --- |
| [Standard Quiver card](../core-concepts/index.md#cards) | Supported |
| [Transform table transform](../cards-transform-table/index.md) | Unsupported |

## Troubleshooting

### A Set math card does not recognize another object set

If an object set in your analysis is not available to select in a Set math card, confirm that its object type matches the card's other input. Set math operates only on object sets of the same type, so object sets of a different type are not listed as selectable inputs. This is the most common reason a Set math card appears to not recognize an object set that is otherwise present in your analysis.

To combine objects that are currently of different types, first bring them to a common type before applying set math. For example, use a [Switch to linked object set](../card-switch-to-linked-object-set/index.md) card to traverse a link from one object type to the other. You can then apply set math to the resulting object sets.

Alternatively, convert the object sets to [Datasets](../card-object-set-dataset/index.md) and use the [Set math (dataset)](../card-set-math-dataset/index.md) card, or convert the cards to [Transform tables](https://www.palantir.com/docs/foundry/quiver/card-set-math/cards-transform-table.md#input-object-sets) and use the [Union (transform table)](../card-union-transform-table/index.md) card. Datasets and Transform tables allow for more flexible analytical operations.