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3,673 views
7 votes
7 votes

Given that

$B(a)$ means “$a$ is a bear”

$F(a)$ means “$a$ is a fish” and

$E(a,b)$ means “$a $ eats $b$”

Then what is the best meaning of

$\forall x [F(x) \to \forall y(E(y,x)\rightarrow b(y))]$

  1. Every fish is eaten by some bear
  2. Bears eat only fish
  3. Every bear eats fish
  4. Only bears eat fish
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3 Answers

11 votes
11 votes

Let us translate the given statement :

For every x,if x is a fish, then for every y, if y eats x then y is bear..

This is enforcing the condition that every animal that eats a fish is a bear.. So only option d matches..


other options:

option a:Every fish is eaten by some bear

$\forall x(F(x)\Rightarrow\exists y(B(y)\wedge E(y,x)))$

ie. for all x, if x is a fish, then there is a y such that y is a bear and y eats x.

option b:Bears eat only fish

$\forall x(B(x)\Rightarrow\forall y (E(x,y)->F(y))$

i.e for every x, if x is a bear,then for all y ,if x eats y, then y is a fish.

option c:Every bear eats fish

$\forall x(B(x)\Rightarrow\exists y (F(y)\wedge E(x,y))$

for all x, if x is a bear, then there is a y such that, y is a fish and x eats y.

edited by
0 votes
0 votes

From the translation of the given statement

For every x,if x is a fish, then for every y, if y eats x then y is bear.

It appears that

Every Bear eats Fish.

Hence the option C is correct.

Answer:

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