2
$\begingroup$

I'm a a bit stumped on symbolizing the sentence: "if only alcohol entices me, then I'm an alcoholic."

My initial thought was that by defining: $E(x)=$ x entices me, $a=$ alcohol, and $A=$ I'm an alcoholic.

Then wouldn't $\forall x(E(x)\land x=a\Rightarrow A$) or $\forall x((E(x)\Leftrightarrow x=a)\Rightarrow A$) work? But after a second thought, it seems like both symbolizations would still hold true even if $x\neq a$, since $(\mathbb{F}\Rightarrow\mathbb{T})\equiv\mathbb{T}$.

So something like the case of $x=$ juice would still make the symbolization true even though it shouldn't according to the original sentence.

Am I doing something wrong by attempting to apply "$\Rightarrow$" even though the original sentence is of the form "if...then..."?

$\endgroup$
1
$\begingroup$

You're very close!

The part 'only alcohol will entice me' translates to $\forall x (E(x) \rightarrow x=a)$, and since that is the antecedent of the conditional, the following will work:

$\forall x (E(x) \rightarrow x=a) \rightarrow A$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.