query: Why are proofs not written as collections of logic symbols but are instead written in sentences?
positive_passages.docid: 27936
positive_passages.text: Why do proof authors use natural language sentences to write proofs?
negative_passages.docid: 109858
negative_passages.text: How could a statement be true without proof?
negative_passages.docid: 19326
negative_passages.text: What makes induction a valid proof technique?
negative_passages.docid: 22584
negative_passages.text: Can we prove that a statement cannot be proved?
negative_passages.docid: 43700
negative_passages.text: Are proofs by contradiction really logical?
negative_passages.docid: 147556
negative_passages.text: Express logic puzzles with proposition calculus notation
negative_passages.docid: 47222
negative_passages.text: Soundness of a rule of a proof system with respect to the truth tables?
negative_passages.docid: 135
negative_passages.text: Difference between "Show" and "Prove"
negative_passages.docid: 103463
negative_passages.text: Mantel's Theorem proof verification
negative_passages.docid: 96504
negative_passages.text: First-Order Logic vs. Second-Order Logic
negative_passages.docid: 126114
negative_passages.text: Adding line by line comments to math proofs
negative_passages.docid: 50178
negative_passages.text: \qed for theorems without proofs
negative_passages.docid: 66366
negative_passages.text: How to change the word "Proof" in the proof environment?
negative_passages.docid: 136734
negative_passages.text: Do truth tables need proofs?
negative_passages.docid: 58065
negative_passages.text: Square brackets in in the `description' of the theorem environment
negative_passages.docid: 46423
negative_passages.text: Distributivity of quantifiers over logical connectives
negative_passages.docid: 85770
negative_passages.text: What is the difference between ∀x(p(x) →q(x)) and ∀x(p(x) ∧q(x))?