query: How can you prove $(P\rightarrow Q)\lor(Q \rightarrow P)$ using natural deduction?
positive_passages.docid: 147375
positive_passages.text: Prove :(P → Q) ∨ (Q → P) using natural deduction
negative_passages.docid: 48368
negative_passages.text: Prove using Natural Deduction in predicate logic $(\forall x\ P(x))\to Q ⊢ \exists x (P(x)\to Q)$
negative_passages.docid: 88104
negative_passages.text: Prove "$(p \lor q) \land (\neg p \lor r)) \rightarrow (q \lor r)$" is a tautology
negative_passages.docid: 91081
negative_passages.text: Prove that, for every natural n, $\sum_{d|n} \frac{\mu(d)}{d}=\prod_{p|n}(1-\frac{1}{p})$
negative_passages.docid: 62224
negative_passages.text: Need help with proof for Dedekind cuts on $\mathbb{Q}^+$
negative_passages.docid: 91861
negative_passages.text: Propositional Logic: p → q, ¬p → r, ¬q → ¬r ⊢ q
negative_passages.docid: 49994
negative_passages.text: Deduction of $\forall y \exists x (x=y)$
negative_passages.docid: 45323
negative_passages.text: How to prove $\vdash\neg P\to (P\to Q)$?
negative_passages.docid: 108704
negative_passages.text: Help with proof of $|x+y| \geq |x|-|y|$
negative_passages.docid: 121361
negative_passages.text: Showing that $\lnot Q \lor (\lnot Q \land R) = \lnot Q$ without a truth table
negative_passages.docid: 18140
negative_passages.text: When does $\,n\mid q^3 \Rightarrow n\mid q\,$?
negative_passages.docid: 35236
negative_passages.text: Proof $p \vdash q \Rightarrow p$
negative_passages.docid: 83752
negative_passages.text: If $p + q = 1$ prove that for any natural $n, m$ following is true: $(1 - p^n)^m + (1 - q^m)^n \ge 1$
negative_passages.docid: 48614
negative_passages.text: Why is "$P \Rightarrow Q$" equivalent to "$\neg Q \Rightarrow \neg P$"?
negative_passages.docid: 32027
negative_passages.text: Given (p ∧ q), use the Fitch system to prove (q ∨ r)
negative_passages.docid: 93707
negative_passages.text: Formal proof for $q \land \neg q \vdash r \land \neg r$
negative_passages.docid: 122684
negative_passages.text: How do you prove Well-Ordering without Mathematical Induction? (and vice-versa)