_____ is the property of an operation and set that the performance of the operation on members of the set always yields a member of the set.
The property described in the question is called closure
The property described in the question is called closure. In mathematics, closure refers to the property that a mathematical operation, when applied to elements from a particular set, always produces a result that belongs to the same set.
To provide a more detailed explanation, let’s consider an example. Suppose we have a set of even numbers {2, 4, 6, 8}, and we define an operation as addition. If we take any two even numbers from the set and perform addition on them, the result will always be an even number. For instance, adding 2 and 4 yields 6, which is also an even number. This illustrates closure under addition for the set of even numbers.
Closure is important in mathematics because it guarantees that when we perform operations on elements of a set, we won’t encounter any elements that don’t belong to the set. It allows us to work exclusively within a particular set, making calculations and proofs more manageable and ensuring the results remain within our desired domain.
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