query: If a choice structure satisfies WARP, then the underlying binary relation is rational.
positive_passages.docid: 19811
positive_passages.text: $(P(X), C_R)$ may be a choice structure even if $R$ is not a rational relation.
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: 12175
negative_passages.text: Applying the principle of equivalence to an accelerated frame
negative_passages.docid: 139064
negative_passages.text: Show by using logical connectives laws that $(P\to Q) \land (Q \to R) $ is equivalent to $(P \to R) \land [(P \iff Q) \lor (R \iff Q)]$
negative_passages.docid: 46430
negative_passages.text: A simple decision problem whose decidability is not known
negative_passages.docid: 109682
negative_passages.text: Proposed proof of: If $A \subset B \subset \bar{A}$ and $A$ is connected, then $B$ is connected
negative_passages.docid: 51863
negative_passages.text: Logical Conditional Truth Table Rationale
negative_passages.docid: 118189
negative_passages.text: Proving the pairing axiom from the rest of ZF
negative_passages.docid: 91281
negative_passages.text: Proving the so-called "Well Ordering Principle"
negative_passages.docid: 62757
negative_passages.text: Showing that a ring is a field as well for one of the provided choices.
negative_passages.docid: 147908
negative_passages.text: Why use the biconditional in the Axiom of Extensionality
negative_passages.docid: 152685
negative_passages.text: Parallel postulate from Playfair's axiom
negative_passages.docid: 115675
negative_passages.text: Strange consequences of Axiom of Choice in Zermelo set theory
negative_passages.docid: 104636
negative_passages.text: Bayesian Decision theory
negative_passages.docid: 132287
negative_passages.text: Axiom of Choice and Right Inverse
negative_passages.docid: 152827
negative_passages.text: Defeating Russell's paradox
negative_passages.docid: 22408
negative_passages.text: Jutifying: irrational + rational = irrational