Last Update: 25 October 2010
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- Every archer has arrows.
∀

*x*[Archer(*x*) → HasArrows(*x*)] - Some archer has no arrows.
∃

*x*[Archer(*x*) ∧ ¬HasArrows(*x*)] - Every archer hits a target.
∀

*x*[Archer(*x*) → ∃*y*[Target(*y*) ∧ Hits(*x*,*y*)]] - Every target is hit by some archer.
∀

*y*[Target(*y*) → ∃*x*[Archer(*x*) ∧ Hits(*x*,*y*)]] - Every archer hits a different target
- (in the sense
that each archer hits only their own target and no other target)

- (get ready now…)

∀

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

*x*_{1}∃*x*_{2}∃*y*[Archer(*x*_{1}) ∧ Archer(*x*_{2}) ∧*x*_{1}≠*x*_{2}∧ Target(*y*) ∧ Hits(*x*_{1},*y*) ∧ Hits(*x*_{2},*y*)] - No archer hits more than one target.
- (if you could read #5, then this one should be easy :-)

¬∃

*x*∃*y*_{1}∃*y*_{2}[Archer(*x*) ∧ Target(*y*_{1}) ∧ Target(*y*_{2}) ∧*y*_{1}≠*y*_{2}∧ Hits(*x*,*y*_{1}) ∧ Hits(*x*,*y*_{2})]

Text copyright © 2010 by William J. Rapaport (rapaport@buffalo.edu)

They are not meant to infringe on any copyrights held by the creators.

For more information on any cartoon, click on it, or contact me.

http://www.cse.buffalo.edu/~rapaport/archer-answers.html-20100927