In mathematics, the symbol ∀ is called the universal quantifier, and when it is written with the variable x, ∀x, it is read as “For all possible values of x. “Expressions that imply the use of the universal quantifier include “any, ““anything, ““anyone, ““everything, ““everyone, ““everybody, ““for every x,” and “for all x.”Using this notation, statements such as “Everything is fine” can be symbolized by rewriting the statement first as “Every x is fine “and then further refining the statement to “For all x, x is fine. If we let F= the term “fine, “then our original statement can now be symbolized as (∀x)(Fx). Express each of the statements in Exercises using this new notation.
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