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It is simply a mapping. It could be a function but there are several conditions that need to be met before the mapping can become a function and there is no basis for assuming that those conditions are met.
A boolean operator is a simple word such as and, or, or not which are used to narrow or expand searches. Boolean operators are also used in programming to determine a path of action often depending on the status of a variable.
The event E must be well defined.
The equation must be written such that the right side is equal to zero. And the resulting equation must be a polynomial of degree 2.
That one may factor under the radical.