# Transcribing from English to Predicate Logic

The question I am trying to answer is:

Transcribe the following to English:

Adam is the tallest one in the class.

Transcription guide:

$$Cx$$: $$x$$ is in the class

$$Txy$$: $$x$$ is taller than $$y$$

$$a$$: Adam

The question also says I have to explicitly state that Adam is not taller than himself. The answer given by the book is,

$$\forall x [(Cx \land x\neq a) \rightarrow Tax]$$,

however I thought this transcribed to 'Adam is taller than everyone in the class that is not himself' which does not say whether he is taller than himself or not. So I said the sentence could be transcribed as,

$$\forall x[Cx \rightarrow (Tax \equiv x \neq a)]$$

or

$$\forall x [(Cx \land x\neq a) \rightarrow Tax] \land \neg Taa$$.

• The first one. $a$ denotes Adam; thsu $Cx \to x \ne a$ means "$x$ is in the Class and he is not Adam". – Mauro ALLEGRANZA Sep 11 '19 at 6:52
• By Exportation, this is the same as : $∀x[Cx → (x≠a \to Tax)]$ that is near to the second one. – Mauro ALLEGRANZA Sep 11 '19 at 6:54
• Don't forget to specify that Adam is in the class. – Graham Kemp Sep 11 '19 at 7:02
• @MauroALLEGRANZA Are you saying that the book's answer is correct or that the first one of my answers is correct? – Lachie Sep 11 '19 at 7:25

If the question explicitly asks you to say that Adam is not taller than himself, than the answer in the book did indeed forget to add the $$\neg Taa$$ statement. So, your second answer is better than the book's. And, your first answer also implies that Adam cannot be taller than himself. So, good for you.
$$\forall x[Cx \rightarrow (Tax \equiv x \neq a)] \land Ca$$
$$\forall x [(Cx \land x\neq a) \rightarrow Tax] \land \neg Taa \land Ca$$