# Operations on sets —Python: Dictionaries and Sets

You've already learned how to create and modify sets. But if we limit ourselves to that, it might seem that sets aren't all that different from lists. Yes, they allow you to check if an item exists more quickly, but they do not support slices. So the richness and power of comparing sets bring the benefit.

## Checking sets for equality

Let's check two sets for equality:

``````set([1, 2, 3, 2, 1]) == {3, 1, 2}  # True
``````

You might think two sets are the same if the second set contains every element of the first one, and your guess would be close to the truth. But remember that collections in Python only store references to objects. So are sets equal if they point to the same objects? Identical references are equal, that's true, but different objects can also be equal.

The fact is that Python has a special equality-checking protocol. Most of the embedded data types support this protocol. We can check the equality of numbers, strings, and boolean values. And we can also make tuples, lists, and dictionaries equal. And that's where Python is good. When we equate two collections of the same type, we consider those collections equal if their elements are equal pairwise (again, from a protocol point of view). Take a look:

``````[1, 2, ["foo", "bar"]] == [1, 2, ["foo"] + ["bar"]]  # True
(1, True, []) == (1, True, [])  # True
{"a": 1, "b": 2} == {"b": 2, "a": 1}  # True
``````

Dictionaries are equal if the order of the keys is different. The sets of keys themselves are the same as long as the values for the corresponding keys are the same. So sets are equal if they contain identical sets of equal elements in pairs.

## Combining sets

Sets in Python, like in mathematics, support the union operation. This operation does not combine sets, as it might seem, but returns a new set. It is an object containing all the items from at least one of the original sets.

In terms of meaning, the union operation is similar to the `OR` operation in Boolean logic: an element is present in the union set if it is present in the first source set OR in the second. Python uses the `|` operator to join sets:

``````visited_by_masha = {'Paris', 'London'}
``````

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