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How do you differentiate between at least one X and exactly one X in predicate logic?

At least one x has F: ExFx

Exactly one x has F: ExVy(Fy <->x=y)

Fx: x is a President.

In that case, "there is at least one President" is "ExFx": and "there is exactly one President" is "ExVy(Fy <->x=y)"

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