# Inverse

## Inverse

When an operation ‡ is defined in a set E, the inverse of a non-zero element x of E is an element denoted by $$n^{-1}$$, such that n ‡ $$n^{-1}$$ = 1.

### Example

• The inverse of $$\dfrac{4}{9}$$ is $$\dfrac{9}{4}$$, since $$\dfrac{4}{9}\space × \space\dfrac{9}{4}\space = \space 1$$.
• Consider the set E = {a, b, c} and the union set operation denoted by $$\bigcup$$. We have {a, b} $$\bigcup$$ {a, b}’ = E, where E is the identity element for the operation of union.