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## Determine whether or not a given set of rational numbers is additively closed

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.1 Exercise 1.1.6 Determine which of the following sets are groups under addition: The set $A_1$ of rational numbers…

## Decide whether or not a given binary operator is commutative

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.1 Exercise 1.1.2 Determine which of the following binary operations are commutative. The operation $\star$ on $\mathbb{Z}$ defined by…

## Decide whether or not a given binary operator is associative

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.1 Exercise 1.1.1 Determine which of the following binary operations are associative. The operation $\star$ on $\mathbb{Z}$ defined by…