query: $\exists x (P(x) \to \forall y P(y))$
positive_passages.docid: 1027
positive_passages.text: Why is this true? $(\exists x)(P(x) \Rightarrow (\forall y) P(y))$
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: 42095
negative_passages.text: Existence in ZF of a set with countable power set
negative_passages.docid: 59724
negative_passages.text: Proving that $x_n\to L$ implies $|x_n|\to |L|$, and what about the converse?
negative_passages.docid: 5293
negative_passages.text: Show that the logic $ \ \forall x \exists y \ P(x,y) \ $ is not logically equivalent to $ \ \exists x \forall y \ P(x,y) \ $
negative_passages.docid: 85818
negative_passages.text: $E(|X-Y|)$ for $X$, $Y$ i.i.d and uniform on $[0,1]$
negative_passages.docid: 37183
negative_passages.text: Show that the set of all $x$ such that $x \in P$ and $x \notin Q$ exists
negative_passages.docid: 140759
negative_passages.text: What is exactly the difference between $\forall x \neg P(x)$ and $\neg \forall xP(x)$?
negative_passages.docid: 129331
negative_passages.text: Prove that $|x^p - y^p| \le p|x-y|(x^{p-1} + y^{p-1})$ provided that $1 \le p \lt \infty$ and $x, y \ge 0$
negative_passages.docid: 136427
negative_passages.text: Given $∃y.∀x.p(x,y)$, use the Fitch system to prove $∀x.∃y.p(x,y)$
negative_passages.docid: 153492
negative_passages.text: Let $p\colon X \to Y$ be a quotient map then if each set $p^{-1}({y})$ is connected, and if $Y$ is connected, then $X$ is connected.
negative_passages.docid: 92290
negative_passages.text: For each $x,y,z∈\mathbb N$, if $x<y$ then $x+z<y+z$
negative_passages.docid: 45481
negative_passages.text: Prove or disprove validity: $(\forall x \exists y (P(x) \supset Q(y))) \supset(\exists y \forall x (P (x) \supset Q(y)))$
negative_passages.docid: 22918
negative_passages.text: What came first, the $\forall$ or the $\exists$?
negative_passages.docid: 45323
negative_passages.text: How to prove $\vdash\neg P\to (P\to Q)$?
negative_passages.docid: 3820
negative_passages.text: Prove that $||x|-|y||\le |x-y|$
negative_passages.docid: 143735
negative_passages.text: Prove/Disprove: For any sets $X$ and $Y$, $\overline{X\cap Y} = \bar{X}\cup\bar{Y}$