query: Can $p ∧ q$, where $p$ and $q$ are propositional variables, be a proposition?
positive_passages.docid: 153440
positive_passages.text: Is logical implication always determinable from just the given statements?
negative_passages.docid: 87955
negative_passages.text: How to prove that $P \rightarrow Q$ is equivalent with $\neg P \lor Q $?
negative_passages.docid: 56351
negative_passages.text: Prove that these statements $(A \lor \neg B)$ and $\neg A \to \neg B$ are logically equivalent
negative_passages.docid: 138897
negative_passages.text: help with some Hilbert style proofs in a propositional logic axiom system.
negative_passages.docid: 116978
negative_passages.text: Trying to prove $p,p \to (r \to q) \vdash (\neg q \to \neg r)$ by using natural deduction.
negative_passages.docid: 84251
negative_passages.text: Show that $\Gamma \cup \{\neg \phi\}$ is satisfiable if and only if $\Gamma\not \models \phi$
negative_passages.docid: 125164
negative_passages.text: How to prove the existence of $b$ in $Q$ such that $a<b^2<c$ in $Q$?
negative_passages.docid: 70552
negative_passages.text: Prove that $\mathcal{P}(A)⊆ \mathcal{P}(B)$ if and only if $A⊆B$.
negative_passages.docid: 72034
negative_passages.text: Truth table and the meaning of $\oplus$ in propositional logic
negative_passages.docid: 19811
negative_passages.text: $(P(X), C_R)$ may be a choice structure even if $R$ is not a rational relation.
negative_passages.docid: 87992
negative_passages.text: A proposition is non-falsifiable. So what?
negative_passages.docid: 141952
negative_passages.text: Is there a decision procedure for intuitionistic propositional logic?
negative_passages.docid: 67717
negative_passages.text: $A \oplus B = A \oplus C$ imply $B = C$?
negative_passages.docid: 63963
negative_passages.text: deductive system where the axioms are all the propositions that are not tautology
negative_passages.docid: 130998
negative_passages.text: Is $\exists x \in A ~:~ P(x)$ the same as $\exists x ~:~ x \in A \implies P(x)$
negative_passages.docid: 77759
negative_passages.text: 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?
negative_passages.docid: 113735
negative_passages.text: Do we need to prove that if x∉A in proposition "if A⊆B then A⋃B=B"?