• More complex examples:

    1. Every archer has arrows.

      ∀x[Archer(x) → HasArrows(x)]

    2. Some archer has no arrows.

      ∃x[Archer(x) ∧ ¬HasArrows(x)]

    3. Every archer hits a target.

      ∀x[Archer(x) → ∃y[Target(y) ∧ Hits(x,y)]]

    4. Every target is hit by some archer.

      ∀y[Target(y) → ∃x[Archer(x) ∧ Hits(x,y)]]

    5. Every archer hits a different target
        (in the sense that each archer hits only their own target and no other target)
          (get ready now…)

      ∀x1∀x2∀y1∀y2{ [ Archer(x1) ∧ Archer(x2) ∧ Target(y1) ∧ Target(y2) ∧ Hits(x1,y1) ∧ Hits(x1,y2) ] → y1=y2}

    6. No archer hits more than one target.
        (if you could read #5, then this one should be easy :-)

      ¬∃x∃y1∃y2[Archer(x) ∧ Target(y1) ∧ Target(y2) ∧ y1≠y2 ∧ Hits(x,y1) ∧ Hits(x,y2)]