query: Interpretation of logic equivalence: $P\rightarrow Q\Leftrightarrow \sim P\vee Q$
positive_passages.docid: 145128
positive_passages.text: Understanding of Material Implication
negative_passages.docid: 22115
negative_passages.text: Equivalent definitions of Boolean Algebras
negative_passages.docid: 46160
negative_passages.text: What is the difference between implication symbols: $\rightarrow$ and $\Rightarrow$?
negative_passages.docid: 5293
negative_passages.text: Show that the logic $ \ \forall x \exists y \ P(x,y) \ $ is not logically equivalent to $ \ \exists x \forall y \ P(x,y) \ $
negative_passages.docid: 41044
negative_passages.text: Equivalence of $a \rightarrow b$ and $\lnot a \vee b$
negative_passages.docid: 108045
negative_passages.text: Show that 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: 75381
negative_passages.text: How can we reason about "if P then Q" or "P only if Q" statements in propositional logic?
negative_passages.docid: 47161
negative_passages.text: Quick logic question about $P\leftrightarrow Q$, terminology
negative_passages.docid: 109318
negative_passages.text: Equivalence relation $(a,b) R (c,d) \Leftrightarrow a + d = b + c$
negative_passages.docid: 67709
negative_passages.text: Stuck with proof for $\forall A\forall B(\mathcal{P}(A)\cup\mathcal{P}(B)=\mathcal{P}(A\cup B)\rightarrow A\subseteq B \vee B\subseteq A)$
negative_passages.docid: 150857
negative_passages.text: Equivalence relations on S given no relation?
negative_passages.docid: 132287
negative_passages.text: Axiom of Choice and Right Inverse
negative_passages.docid: 32180
negative_passages.text: Why is "$A$ unless $B$" equivalent to $A \lor B$?
negative_passages.docid: 153634
negative_passages.text: A statment about the equivalence between the Axiom of Choice and the surjectivity of the projections.
negative_passages.docid: 70409
negative_passages.text: Rational Equivalence Relation and Measure
negative_passages.docid: 108292
negative_passages.text: Precedence between implication and bi-implication