Why if the antecedent P is false, and the consequence Q true, then the implication P $\Rightarrow$ Q is true?
101877
Assumed True until proven False. The Curious Case of the Vacuous Truth
56325
If we accept a false statement, can we prove anything?
32027
Given (p ∧ q), use the Fitch system to prove (q ∨ r)
143627
Use the Fitch system to prove the tautology (p ∨ ¬p)
34478
If $P(A \mid E) > P(B \mid E)$ and $P(A \mid \neg E) > P(B \mid \neg E)$, then is $P(A) > P(B)$ true?
136577
In formal logic, how is it possible for an argument with a contradictory conclusion to be valid?
51369
Natural deduction proof of $p \lor (p\implies q)$ with propositional calculus
37196
"If P, then Q; If P, then R; Therefore: If Q, then R." Fallacy and Transitivity
109685
An invalid argument, the conclusion of which is a tautology
100844
How should I understand "$A$ unless $B$"?
31299
Using the Fitch system, how do I prove $((p \implies q) \implies p)\implies p$?
47161
Quick logic question about $P\leftrightarrow Q$, terminology
32244
Propositional Logic - Deduction
88104
Prove "$(p \lor q) \land (\neg p \lor r)) \rightarrow (q \lor r)$" is a tautology
93742
Show that the conditional statement is a tautology without using a truth table
6166
Is the following statement provable?
153440
Is logical implication always determinable from just the given statements?