I have a statement along the gist of "Each member of A is either Y, Z, or both"

Would the appropriate way to write this using first-order logic be:

∀x (A(x) → (Y(x) ∨ Z(x)))

Would it suffice to just use a disjunction here? Or would this be written as

∀x (A(x) → (Y(x) ∨ Z(x)) ∨ (Y(x) ∧ Z(x)))

or is this redundant?

  • $\begingroup$ don't you know what a disjunction exactly is ? $\endgroup$
    – Physor
    Oct 13, 2020 at 17:33

1 Answer 1


Since $(A \land B) \implies (A \lor B)$ the second clause in $ (Y(x) \lor Z(x)) \lor (Y(x) \land Z(x))$ is redundant.


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