query: Prove as equivalents (axiom of choice)
positive_passages.docid: 20252
positive_passages.text: The Axiom of Choice and the Cartesian Product.
negative_passages.docid: 151038
negative_passages.text: How to prove (A v B), (A → C), (B → D) therefore (C v D)
negative_passages.docid: 25997
negative_passages.text: Conditions Equivalent to Injectivity
negative_passages.docid: 108045
negative_passages.text: Show that are logically equivalent
negative_passages.docid: 32180
negative_passages.text: Why is "$A$ unless $B$" equivalent to $A \lor B$?
negative_passages.docid: 102202
negative_passages.text: The smallest infinity and the axiom of choice
negative_passages.docid: 89506
negative_passages.text: Union of disjoint sets : Equivalence relations
negative_passages.docid: 81509
negative_passages.text: The cardinality of a countable union of countable sets, without the axiom of choice
negative_passages.docid: 83757
negative_passages.text: Is the following equivalent to the axiom of choice?
negative_passages.docid: 150790
negative_passages.text: Prove two sets have same Cardinality by writing down bijection
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: 132046
negative_passages.text: Looking for Cantor's original proof of the Cantor-Bernstein theorem that relies on the axiom of choice?
negative_passages.docid: 17624
negative_passages.text: Axiom of Choice iff Every set has a choice function
negative_passages.docid: 58631
negative_passages.text: Continuity and the Axiom of Choice
negative_passages.docid: 48213
negative_passages.text: proving logical equivalence $(P \leftrightarrow Q) \equiv (P \wedge Q) \vee (\neg P \wedge \neg Q)$
negative_passages.docid: 138897
negative_passages.text: help with some Hilbert style proofs in a propositional logic axiom system.
negative_passages.docid: 84562
negative_passages.text: Proof using only field axioms