First Order Logic

Question

Comments

How to interpret this??

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https://gateoverflow.in/95818/tifr2017-b-11

https://gateoverflow.in/112696/testbook-4-qno-27

https://gateoverflow.in/331314/isro2020-73

Answer 1

$B(x)\rightarrow$ x is a bear

$F(x)\rightarrow$ x is a fish

$E(x,y)\rightarrow$ x eats y

Now, the Predicate logic $\forall x\left \{ F(x)\rightarrow \forall y\left \{ E(y,x)\rightarrow B(y) \right \} \right \}$

This says " For every x if x is a fish then if it is eaten by y then that y is only bear "

Which can be translated simply as 

$\rightarrow$ Only Bears can eat fish .

OR

$\rightarrow$ Those who eat fish are bears.

Comments

c thz

https://gateoverflow.in/101834/prepositional-logic-1-1

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@kapil, @gateset
 " y is only bear  "

How did u conclude ONLY  from the Propositional Logic ?
 

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@Dq

See the translation:

For every x, if x is a fish then, for every y, if x is eaten by y then that y is bear.

Based on this statement, option B and C seem to be the probable choices. Now you have to eliminate one. At first look, option B might seem correct.

Now see - for every x, if y eats x, then y is bear. It clearly means, if someone eats fish, then it has to be a bear and no one else (visualise the scenario a bit).

This means that only bears can eat fish, which is a subset of the statement "Every bear eats fish".

So, option C is stricter and hence the answer.