query: Proof that the formula $((p\to q)\land (q\to r)\land p)\to r$ is a tautology
positive_passages.docid: 155381
positive_passages.text: Can anyone help me with a solution?
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: 88104
negative_passages.text: Prove "$(p \lor q) \land (\neg p \lor r)) \rightarrow (q \lor r)$" is a tautology
negative_passages.docid: 140194
negative_passages.text: Using natural deduction to prove that $p \implies q \vdash \lnot p \lor q$
negative_passages.docid: 15312
negative_passages.text: Show that $R \cap R^{−1}$ is an equivalence relation on $X$?
negative_passages.docid: 46939
negative_passages.text: Natural deduction, Proof $\vdash$ $P\Rightarrow(Q\Rightarrow P)$
negative_passages.docid: 111862
negative_passages.text: Proof for sequent (Logic)
negative_passages.docid: 12949
negative_passages.text: Inductive Proof of Euler's Formula $v-e+r=2$
negative_passages.docid: 93410
negative_passages.text: How to prove ~ (~P & ~Q) : P ∨ Q by natural deduction
negative_passages.docid: 10540
negative_passages.text: Prove $\vdash \neg(\square F\land p)$ in $KD$
negative_passages.docid: 56878
negative_passages.text: Proof that $a\mid b \land b\mid c \Rightarrow a\mid c $
negative_passages.docid: 144266
negative_passages.text: set theory proof of $A\cap B = A \setminus(A\setminus B)$
negative_passages.docid: 62755
negative_passages.text: The simplest way of proving that $|\mathcal{P}(\mathbb{N})| = |\mathbb{R}| = c$
negative_passages.docid: 34768
negative_passages.text: Proving $(p \oplus q) \oplus r=p \oplus (q \oplus r)$
negative_passages.docid: 104484
negative_passages.text: Prove that $r$ is a primitive root modulo $p$ if and only if $r^{(p−1)/q}\not\equiv 1\pmod{p}$
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: 91861
negative_passages.text: Propositional Logic: p → q, ¬p → r, ¬q → ¬r ⊢ q