query: Show that for any subset $C\subseteq Y$, one has $f^{-1}(Y\setminus C) = X \setminus f^{-1}(C)$
positive_passages.docid: 65923
positive_passages.text: How to approach proving $f^{-1}(B\setminus C)=A\setminus f^{-1}(C)$?
negative_passages.docid: 78698
negative_passages.text: Prove if $f$ has a right inverse function: $f\circ g=id_x$ $\iff$ $f$ is onto $Y$
negative_passages.docid: 45555
negative_passages.text: $(x+y)^c\le x^c+y^c$ for $0<c\le1$
negative_passages.docid: 6291
negative_passages.text: Proving something is a linearly independent subset
negative_passages.docid: 132541
negative_passages.text: Showing ${1\over n}\sum|S_i|=O(\sqrt n)$ for $S_i\subset [n]$, $|S_i\cap S_i|\le 1$ for $i\ne j$
negative_passages.docid: 13136
negative_passages.text: Element chasing proof that $(A\setminus C)\setminus(B\setminus C) = (A\setminus B)\setminus C$
negative_passages.docid: 93102
negative_passages.text: prove that $f:X\rightarrow Y$ is surjective if and only if $f(f^{-1}(C))=C$
negative_passages.docid: 33524
negative_passages.text: Prove the following $A \setminus (B\setminus C) = (A\setminus B)\cap (A \cup C)$
negative_passages.docid: 111024
negative_passages.text: Does $gHg^{-1}\subseteq H$ imply $gHg^{-1}= H$?
negative_passages.docid: 144693
negative_passages.text: Show that if $B \subseteq C$, then $\mathcal{P}(B) \subseteq \mathcal{P}(C)$
negative_passages.docid: 43504
negative_passages.text: Proving the existence of a complement subspace $U' \subset V$.
negative_passages.docid: 62077
negative_passages.text: Prove that if $W_1\subseteq V$ finite-dimensional, then there is $W_2\subseteq V$ such that $V=W_1\oplus W_2$
negative_passages.docid: 70311
negative_passages.text: Trying to prove (A ∩ B) − C = (A − C) ∩ (B − C)
negative_passages.docid: 80827
negative_passages.text: Let $A$ be a nonempty subset of $\mathbb{R}$. Prove...
negative_passages.docid: 143354
negative_passages.text: Prove that there exists $c\in\mathbb{R}$ such that $f'(c)=f(c)$
negative_passages.docid: 139537
negative_passages.text: Show that $x\subseteq y \Leftrightarrow \mathcal{P}(x)\subseteq\mathcal{P}(y)$.
negative_passages.docid: 154001
negative_passages.text: $(g\circ f)^{-1}=f^{-1}\circ g^{-1}$