query: Help with set theory proofs ((For all A, B ⊆ X: f ( A \ B ) = f ( A ) \ f ( B ))  f is injective)
positive_passages.docid: 25997
positive_passages.text: Conditions Equivalent to Injectivity
negative_passages.docid: 77286
negative_passages.text: Proving set theory question
negative_passages.docid: 93040
negative_passages.text: $f$ is surjective iff it has a right inverse: using the axiom of choice and errors in ProofWiki
negative_passages.docid: 1821
negative_passages.text: Proving $f(C) \setminus f(D) \subseteq f(C \setminus D)$ and disproving equality
negative_passages.docid: 64320
negative_passages.text: Prove that if $0<a<Pr(A)$ then there exists $B\subset A$ such that $Pr(B)=a$
negative_passages.docid: 9158
negative_passages.text: Proving that a propositional theory of any cardinality has an independent set of axioms
negative_passages.docid: 148500
negative_passages.text: Understanding this theorem and how to go about proving it surjectivity?
negative_passages.docid: 50939
negative_passages.text: If $A$ and $B$ are nonempty sets, prove that $A \times B = B \times A$ if and only if $A = B$
negative_passages.docid: 146188
negative_passages.text: Why does a proof of $\exists f: X\to Y$ injection $\iff \exists g: Y \to X$ surjection requires the axiom of choice?
negative_passages.docid: 53551
negative_passages.text: $f(A\cap B)=f(A)\cap f(B)$ $\iff$ $f$ is injective.
negative_passages.docid: 72694
negative_passages.text: Proving that $f(x) = g(x)$ for some $x \in [a,b]$ if $f,g$ continuous, $f(a)  g(b)$
negative_passages.docid: 21391
negative_passages.text: Proving Functions are Surjective
negative_passages.docid: 132971
negative_passages.text: Prove that $|a| < b \iff -b<a<b$
negative_passages.docid: 154363
negative_passages.text: Prove that $\text{aff}(X) = \text{aff}(\text{closure}(X))$
negative_passages.docid: 6825
negative_passages.text: If $f: \mathbb Q\to \mathbb Q$ is a homomorphism, prove that $f(x)=0$ for all $x\in\mathbb Q$ or $f(x)=x$ for all $x$ in $\mathbb Q$.
negative_passages.docid: 52787
negative_passages.text: If $\bigcup F = A$ then $A\in F$ then prove that $A$ has exactly one element
negative_passages.docid: 91947
negative_passages.text: Proof of $ f:I_n \rightarrow I_m \Rightarrow n = m$