I am reading from "Discrete Mathematics and Its applications" by Kenneth H. Rosen, 7th edition. Consider the highlighted part in the following example taken from the same book:
Question Use predicates and quantifiers to express the system specifications “Every mail message larger than one megabyte will be compressed” and “If a user is active, at least one network link will be available.”
Solution: Let S(m, y) be “Mail message m is larger than y megabytes,” where the variable x has the domain of all mail messages and the variable y is a positive real number, and let C(m) denote “Mail message m will be compressed.” Then the specification “Every mail message larger than one megabyte will be compressed” can be represented as ∀m(S(m, 1) → C(m)). Remember the rules of precedence for quantifiers and logical connectives! Let A(u) represent “User u is active,” where the variable u has the domain of all users, let S(n, x) denote “Network link n is in state x,” where n has the domain of all network links and x has the domain of all possible states for a network link. Then the specification “If a user is active, at least one network link will be available” can be represented by
∃uA(u) → ∃nS(n, available).
"Existential quantifier" ∃u is used here, So I think, it should be ∃uA(u)∧ ∃nS(n, available) in place of ∃uA(u) → ∃nS(n, available).
Generally, we use 'implication' with 'universal quantifier' as shown in ∀m(S(m, 1) → C(m)).
Please correct me, if I am wrong.