query: Simplify this expression: $ \left((p\to q) \land (q \to r)\right)\to (p \to r)$
positive_passages.docid: 52585
positive_passages.text: How to prove that $[(p \to q) \land (q \to r)] \to (p \to r)$ is a tautology without using the truth table?
negative_passages.docid: 148571
negative_passages.text: Simplify function notation
negative_passages.docid: 18854
negative_passages.text: Convert an expression to a Function
negative_passages.docid: 49999
negative_passages.text: Express $y$ from $\ln(x)+3\ln(y) = y$
negative_passages.docid: 76685
negative_passages.text: Determine $\text{Aut}(S)$ where $S = \mathbb{Q}[x]/(x^2)$
negative_passages.docid: 43703
negative_passages.text: Find $\lim _{x\to \infty }\left(x\left(\ln\left(x+1\right)-\ln x\right)\right) $
negative_passages.docid: 145578
negative_passages.text: How find the value $\beta$ such $\left|\frac{p}{q}-\sqrt{2}\right|<\frac{\beta}{q^2}$
negative_passages.docid: 44856
negative_passages.text: Can I simplify (solve) a certain DifferenceRoot expression?
negative_passages.docid: 70117
negative_passages.text: Show that $(p \to q) \lor (q \to p)$ is a tautology
negative_passages.docid: 65645
negative_passages.text: Express $w$ and $\frac1w$ for $w=\frac {\sqrt2+\sqrt3}{\sqrt5-\sqrt3}$ in the simplest form with a rational denominator
negative_passages.docid: 51679
negative_passages.text: Simplifying the product $\prod\limits_{k=2}^n \left(1-\frac1{k^2}\right)$
negative_passages.docid: 64484
negative_passages.text: Left ideal $I$ is a direct summand of $R$ iff $I = Rr$, $r^2 = r$
negative_passages.docid: 7066
negative_passages.text: Calculate simple expression: $\sqrt[3]{2 + \sqrt{5}} + \sqrt[3]{2 - \sqrt{5}}$
negative_passages.docid: 103310
negative_passages.text: Evaluation of the following expression
negative_passages.docid: 156597
negative_passages.text: Proving a reduction formula for the antiderivative of $\cos^n(x)$
negative_passages.docid: 1483
negative_passages.text: Left/Right across multi-line equation
negative_passages.docid: 109318
negative_passages.text: Equivalence relation $(a,b) R (c,d) \Leftrightarrow a + d = b + c$