Why do we need to define the value of $p \implies q$ when $p$ is false?
108488
Why aren't vacuous truths just undefined?
35370
Why is this proposition provable and its converse not?
578
In classical logic, why is $(p\Rightarrow q)$ True if both $p$ and $q$ are False?
68607
Could an argument with false Premises and a true Conclusion be logically valid?
109858
How could a statement be true without proof?
77759
How do i prove that $(p \vee q) \wedge (\neg p \vee r) \rightarrow (q \vee r)$ is a tautology without using the truth table?
132423
Non trivial valuation over a finite extension $F/\mathbb{Q}_p$ is equivalent to the one induced by $v_p$
19811
$(P(X), C_R)$ may be a choice structure even if $R$ is not a rational relation.
122015
"This statement is false" - Propositional Logic
109778
Proving $(x-c)|(p(x)-p(c))$
48614
Why is "$P \Rightarrow Q$" equivalent to "$\neg Q \Rightarrow \neg P$"?
113605
In Fitch, how does one prove "(P → Q)" from the premise "(¬P ∨ Q)"?
51369
Natural deduction proof of $p \lor (p\implies q)$ with propositional calculus
1027
Why is this true? $(\exists x)(P(x) \Rightarrow (\forall y) P(y))$
68265
Why is it sensical for a proposition with a false antecedent to validate to true?
45481
Prove or disprove validity: $(\forall x \exists y (P(x) \supset Q(y))) \supset(\exists y \forall x (P (x) \supset Q(y)))$
47161
Quick logic question about $P\leftrightarrow Q$, terminology