Predicate logic - First order logic convert to natural language.

Elementstv

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Feb 6, 2021
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Can anyone please help me translate this into an English phrase. I am greek and this excercise is in Greek so I translated it as best as I could.
Consider the given universe as the sum of all people(meaning that x, y, z refer to people) and interpret E(x,y) as "x trusts y". Translate the following into natural language :

∃x[E(x,x)∧(∀y(E(x,y)↔∀z(E(y,z)↔z≈y))→∀z(E(x,z)↔z≈x))]

Is there anyone that can tackle this problem ?
 
Consider the given universe as the sum of all people(meaning that x, y, z refer to people) and interpret E(x,y) as "x trusts y". Translate the following into natural language :
∃x[E(x,x)∧(∀y(E(x,y)↔∀z(E(y,z)↔z≈y))→∀z(E(x,z)↔z≈x))]
Here is a very stilted translation.
There is a person X such that (X trusts X and X trusts every Y iff every Z is trusted by Y iff Z is equivalent Y) implies (every Z trusted by X iff Z equiv X).
That does not make a whole lot of sense. Now did have to guess as to what \(\approx\) means because not a standard in natural language.
 
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