# Two Ring is Boolean Ring

## Theorem

Let $2$ be the two ring.

Then $2$ is a Boolean ring.

## Proof

From Ring of Integers Modulo m is Ring, $2$ is a ring with unity.

Furthermore, the identities:

$0 \cdot 0 = 0$
$1 \cdot 1 = 1$

show that $2$ is also an idempotent ring.

Hence the result, by definition of Boolean ring.

$\blacksquare$