The relational operators !=, <, <=, ==, >=, and > can all be applied to sets and frozen sets. Because Python automatically converts between sets and frozen sets when necessary, it is possible to have a set on one side of the operator and a frozen set on the other side.

Sets are compared by containment: a set $S$ is considered less than a set $T$ if all of $S$'s elements are in $T$, and $T$ also has at least one other element. For instance, {4, 5} < {3, 4, 5, 6} is true, but {4, 5} < {3, 4, 15, 16} is false. Because of this choice, it is possible for two sets to be incomparable. For example, {1, 2} <= {2, 3} is false, but so is {1, 2} >= {2, 3}.

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