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On existing problems and arbitrary problems in mathematics.
First, the difference between the conditions of establishment

Existence means that among all the elements in a set, it is enough to have one or more coincidence, that is, at least one coincidence.

Arbitrary means that all elements in a set are consistent, that is, no element is consistent.

Second, express the difference between conformity

"arbitrary":? ; "Being":

Third, the difference between quantifiers.

It is a mathematical symbol of existence, which means existence. However, the meaning of all or each is arbitrary. The former is a special quantifier and the latter is a complete quantifier.