query: If $P$ is false, and $Q$ is true, then why does $P \implies Q$?
positive_passages.docid: 15504
positive_passages.text: In classical logic, why is $(p\Rightarrow q)$ True if $p$ is False and $q$ is True?
negative_passages.docid: 137494
negative_passages.text: Why is "If ψ ∈ Γ then the sequent (Γ ⊢ ψ) is correct" true?
negative_passages.docid: 67717
negative_passages.text: $A \oplus B = A \oplus C$ imply $B = C$?
negative_passages.docid: 129185
negative_passages.text: Understanding the truth value for ⇏ when antecedent is false and consequent is true.
negative_passages.docid: 54791
negative_passages.text: Is it true or false that $\lvert P([0, 1]) \setminus P((0, 1)) \rvert > \lvert P(\mathbb{N}) \rvert$
negative_passages.docid: 42150
negative_passages.text: Prove that $\forall x \neg P(x) \iff \neg \exists x P(x)$
negative_passages.docid: 116527
negative_passages.text: Validating a proof for necessary and sufficient conditions on sets A & B such that $P(A) \cup P(B) = P(A\cup B)$
negative_passages.docid: 123458
negative_passages.text: Prove $( \lnot C \implies \lnot B) \implies (B \implies C)$ without the Deduction Theorem
negative_passages.docid: 37183
negative_passages.text: Show that the set of all $x$ such that $x \in P$ and $x \notin Q$ exists
negative_passages.docid: 136577
negative_passages.text: In formal logic, how is it possible for an argument with a contradictory conclusion to be valid?
negative_passages.docid: 65379
negative_passages.text: Deriving $\neg R$ from $\{R↔(R∨(P∧¬P)), R↔¬P, ¬P→(P↔(Q→Q)), P→Q\}$
negative_passages.docid: 4027
negative_passages.text: Why does the material conditional have the truth table it does?
negative_passages.docid: 87928
negative_passages.text: Proof of logical equivalence of biconditional and other proposition
negative_passages.docid: 35370
negative_passages.text: Why is this proposition provable and its converse not?
negative_passages.docid: 148237
negative_passages.text: Is ¬¬(¬¬P → P) provable in intuitionistic logic?
negative_passages.docid: 140194
negative_passages.text: Using natural deduction to prove that $p \implies q \vdash \lnot p \lor q$
negative_passages.docid: 122015
negative_passages.text: "This statement is false" - Propositional Logic