# Tagged: Relation

## Demonstrate that a given relation defined in terms of a surjective function is an equivalence relation

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 0.1 Exercise 0.1.7 Let $f : A \rightarrow B$ be a surjective map of sets. Prove that the relation $\sim$ on $A$ given...

## Determine whether a given relation is well defined

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 0.1 Exercise 0.1.6 Determine whether the function $f : \mathbb{R}^+ \rightarrow \mathbb{Z}$ given by mapping a real number $r$ to the first digit...

## Determine whether given relations are well-defined

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 0.1 Exercise 0.1.5 Determine whether the following functions are well defined. $f : \mathbb{Q} \rightarrow \mathbb{Z}$ given by $f(a/b) = a$. This relation...