HW2 Problem 10

Problem 10

Give a set different from any of those described in the examples of the text and not a set of numbers. Define two different binary operations $*$ and $*'$ on this set. Be sure that your set is well-defined.

Solution

Let $S=\{green, purple\}$. Define $*$ on $S$ as $a*b=purple$ and $*'$ on $S$ as $a*'b=green$ for all $a,b \in S$.