query: If $ f $ is injective and $ g $ is injective, then $ f \circ g $ is surjective.
positive_passages.docid: 21391
positive_passages.text: Proving Functions are Surjective
negative_passages.docid: 16092
negative_passages.text: How to prove that the composition of two surjective functions is surjective
negative_passages.docid: 106809
negative_passages.text: $f: G→G$ defined by $f(x) =x^2$ is a homomorphism if and only if $G$ is abelian.
negative_passages.docid: 101042
negative_passages.text: Suppose we have functions $f:A→B$ and $g:B→C$. Prove that if $f$ and $g$ are invertible, then so is $g \circ f$.
negative_passages.docid: 56278
negative_passages.text: $I$ and $J$ are coprime ideals iff $x \to (x + I, x + J)$ is surjective.
negative_passages.docid: 11798
negative_passages.text: If $f \circ g$ is onto then $f$ is onto and if $f \circ g$ is one-to-one then $g$ is one-to-one
negative_passages.docid: 56413
negative_passages.text: $f(g(x))=g(f(x))$ implies $f(c)=g(c)$ for some $c$
negative_passages.docid: 76674
negative_passages.text: Let $S:U\rightarrow V, \ T:V\rightarrow W$ and if $S$ and $T$ are both injective/surjective, is $T\circ S$ injective/surjective?
negative_passages.docid: 58642
negative_passages.text: If $g \circ f$ is the identity function, then which of $f$ and $g$ is onto and which is one-to-one?
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: 130363
negative_passages.text: Prove composition of two surjections is surjection
negative_passages.docid: 53551
negative_passages.text: $f(A\cap B)=f(A)\cap f(B)$ $\iff$ $f$ is injective.
negative_passages.docid: 73526
negative_passages.text: The equivalence of "Every surjection has a right inverse" and the Axiom of Choice
negative_passages.docid: 129452
negative_passages.text: Groups $G,H$ with surjective homomorphisms that are quotient of each other
negative_passages.docid: 10024
negative_passages.text: How to prove $(f \circ\ g) ^{-1} = g^{-1} \circ\ f^{-1}$? (inverse of composition)
negative_passages.docid: 5635
negative_passages.text: How to prove that the Frobenius endomorphism is surjective?
negative_passages.docid: 65977
negative_passages.text: Showing function is injective iff $f(M_1 \cap M_2) = f(M_1)\cap f(M_2)$