Test by Bikram | Mock GATE | Test 4 | Question: 55

Question

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?

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

• A.   Marlyn hates everybody except Michael.
• B.   Marlyn only hates Michael.
• C.   Marlyn loves everybody except Michael.
• D.   Marlyn is loved only by Michael.

Answer 1

∀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".

Comments

sir, y option d is failing?

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∀x(x≠Michael→Hate(Marlyn,x))

P = x≠Michael

Q = Hate(Marlyn,x)

∀x(P-->Q)

If x is not michael(P = True) then marlyn hates x(RHS = True)

But if x is michael i.e (P = false) then Qx can be true / false ..i.e Marlyn may or may not hate Michael

please correct if wrong 

@Shaik Masthan