Chapter 8.3, Problem 58ES

To determine

Consider the set of elements $\left\{a,b,c,d\right\}$ with the operation $\nabla$ as given in the following table

$\nabla$	$a$	$b$	$c$	$d$
$a$	$d$	$a$	$b$	$c$
$b$	$a$	$b$	$c$	$d$
$c$	$b$	$c$	$d$	$a$
$d$	$c$	$d$	$a$	$b$

In order to compute $c\nabla d$, find $c$ in the left column and align it with $d$ in the top row. The result is $a$.

Find the inverse of each element.