Discrete Structures

Archer Sentences: Answers

Last Update: 25 October 2010

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  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

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

  6. No archer hits more than one target.

    ¬∃xy1y2[Archer(x) ∧ Target(y1) ∧ Target(y2) ∧ y1y2 ∧ Hits(x,y1) ∧ Hits(x,y2)]

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