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Answer :
The symbol for the unique existence quantifier is ∃!, and it is used to express that there exists exactly one object that satisfies a given condition, such as the definition of a function.
The symbol for the "unique existence" quantifier is ∃! (read as "there exists a unique"). This quantifier is used to express that there is exactly one object that satisfies a given condition.
Let's take the example of the definition of a function. In mathematics, a function is defined as a relation between a set of inputs, called the domain, and a set of outputs, called the range, such that each input is associated with exactly one output. We can use the unique existence quantifier to express this definition concisely.
For instance, if we have a function f(x) = x^2, we can use the unique existence quantifier to state that "there exists a unique y such that y = x^2 for any given x."
To symbolize this statement using the unique existence quantifier, we can write it as: ∃!y (y = x^2)
In this case, the quantifier ∃! is used to indicate that there exists a unique value of y (the output) such that y is equal to x^2.
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