An adversary that is capable of collecting and exploiting information and has expressed the intent to do so is considered a
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No. Closure is the property of a set with respect to an operation. You cannot have closure without a defined set and you cannot have closure without a defined operation.
Multiplication is the inverse operation of division when the latter is defined.
The answer depends on the operation that is defined on the group.
Undefined: You cannot divide by zero
Provided the domains are defined in an appropriate manner, subtraction is the inverse operation of addition while division is the inverse operation of multiplication.