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Consider the proposition given below:

$\text{Hate} (a, b)$ denotes $a$ hates $b$.

What is the correct translation of the below mentioned First Order Logic statement?

$\forall x( x \neq  Michael \rightarrow Hate (Marlyn, x))$

  1.   Marlyn hates everybody except Michael.
  2.   Marlyn only hates Michael.
  3.   Marlyn loves everybody except Michael.
  4.   Marlyn is loved only by Michael.
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∀x$\left ( x\neq Michael \rightarrow Hate \left ( Marlyn, x \right ) \right )$

$x$ is the domain of all the people

For every $x$, if $x$ is not the Michael then Marlyn hates everyone, this predicate function will return true

One other way to say this statement "Marlyn hates everyone except Michael".

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