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32 votes
32 votes

Given that

  • $B(x)$ means "$x$ is a bat",
  • $F(x)$ means "$x$ is a fly", and
  • $E(x, y)$ means "$x$ eats $y$",

what is the best English translation of $$ \forall x(F(x) \rightarrow \forall y (E(y, x) \rightarrow B(y)))?$$

  1. all flies eat bats
  2. every fly is eaten by some bat
  3. bats eat only flies
  4. every bat eats flies
  5. only bats eat flies
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3 Answers

Best answer
40 votes
40 votes
If $x$ is a fly, then for all $y$ which eats $x$, $y$ is a bat. This means only bats eat flies.

Option (E).
edited by
11 votes
11 votes
For any/all x if it is a fly and if it gets eaten up by any y than that y must be a bat..

So only bats eat flies.

Option e
3 votes
3 votes

first solve ∀y(E(y,x)→B(y)) only take x=fly1

so for x1fly1  ∀y(E(y,x)→B(y)) telling that : (if y1 eats fly1  then y1 is Bat) and(if y2 eats fly1  then y2 is Bat) and (if y1 eats fly1  then y1 is Bat ) and ....(if yn eats fly1  then yn is Bat).

this conclude that:  only bats eats fly1 .

no solve comlete :∀x(F(x)→∀y(E(y,x)→B(y)))

 = (if x is fly1 then only bats eats fly1) and (if x is fly2 then only bats eats fly2) and (if x is fly3 then only bats eats fly3)...

= every fly  eaten by bats only.

= only bats eats flies.

Ans: E

 

Answer:

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