Could we build a truth table of "$P \Rightarrow \lnot P$"? What is its meaning and its Venn Diagram? The usual truth table of $P \Rightarrow Q$ looks like this




$P$
$Q$
$P \Rightarrow Q$




True
True
True


True
False
False


False
True
True


False
False
True




Before determine the truth or false of $P \Rightarrow Q$.
$P \Rightarrow Q$ is like a claim.
And when we are sure that there is no way to have a condition where
$P$ is true and $Q$ is false.
Until now the claim is considered true.
Is an implication of the form $P \Rightarrow \lnot P$ valid or not valid?
What I mean by "valid" is from the quote in a book "How to prove it by D.J. Vellman".

We will say that an argument is valid if the premises cannot all be true without the conlcusion being true ads well.

At a guess, does the truth table look like this?




$P$
$\lnot P$
$P \Rightarrow \lnot P$




True
False
False


False
True
True




But what is its meaning and venn diagram?
There's a venn diagram by hand.
https://imgur.com/a/behSgSw


P ⇒ ¬P is a contradiction and therefore it's invalid. I mean, if P is true then P is... not true? But we just said P is true. That doesn't work and therefore a truth table can't be constructed.
