I trying to come up with a valid formalisation of the quote "You can fool all the people some of the time, and some of the people all the time, but you cannot fool all the people all the time".
I have the following expression which I believe to be a correct answer:
(∀p.∃t.𝖥𝗈𝗈𝗅(p,t)) ∧ (∃p.∀t.𝖥𝗈𝗈𝗅(p,t)) ∧ ¬∀p.∀t.𝖥𝗈𝗈𝗅(p,t)
The above expression states that all people will be fooled for some time AND some people will be fooled for all of the time AND not all people will be fooled all of the time. I think the expression is correct because it covers all the scenarios in the quote.
However, I am not sure if my reasoning is correct. Any insights are appreciated.