Why is the implication $P \Rightarrow Q$ false if and only if $P$ is true and $Q$ is false?
578
In classical logic, why is $(p\Rightarrow q)$ True if both $p$ and $q$ are False?
35370
Why is this proposition provable and its converse not?
13012
Why can a = b imply 2 = 1?
100844
How should I understand "$A$ unless $B$"?
52322
Implication in mathematics - How can A imply B when A is False?
150053
Is "$(P \land Q) \to P$" a tautology?
17073
Using proof by contradiction vs proof of the contrapositive
13064
In what order are chained implications evaluated? (i.e. $a \implies b \implies c$)
35236
Proof $p \vdash q \Rightarrow p$
78009
Why can't we use implication for the existential quantifier?
5293
Show that the logic $ \ \forall x \exists y \ P(x,y) \ $ is not logically equivalent to $ \ \exists x \forall y \ P(x,y) \ $
20789
If $\Sigma \vdash \varphi$ then $\Sigma \vdash \forall x \varphi$. Why when $(\varphi \implies \forall x \varphi)$ is not true?
121361
Showing that $\lnot Q \lor (\lnot Q \land R) = \lnot Q$ without a truth table
45481
Prove or disprove validity: $(\forall x \exists y (P(x) \supset Q(y))) \supset(\exists y \forall x (P (x) \supset Q(y)))$
122015
"This statement is false" - Propositional Logic
137494
Why is "If ψ ∈ Γ then the sequent (Γ ⊢ ψ) is correct" true?
48213
proving logical equivalence $(P \leftrightarrow Q) \equiv (P \wedge Q) \vee (\neg P \wedge \neg Q)$