Ä-operation $(a_{i}, a_{j}) \in {a}$	Å-operation $(a_{i}, a_{j}) \in {a}$
1) $(a_{i} \otimes a_{i}) = (a)$	1) $(a_{i} \oplus a_{i}) = 0$
2) $(a_{i}, a_{j}) \in {a}$ $(a_{i} \otimes a_{j}) = (a_{j} \otimes a_{i})$	2) $(a_{i} \oplus a_{j}) = (a_{j} \oplus a_{i})$ If ${(a_{i} \oplus a_{j})}_{\oplus} = [(a_{i} \oplus a_{j}) \oplus a_{k}]$ $\to$ ${(a_{i} \oplus a_{j})}_{\oplus} \neq {(a_{j} \oplus a_{i})}_{\oplus}$
3) $(n, m) \in N$ $(n a_{i} \otimes a_{j}) = n (a_{i} \otimes a_{j})$ $(n a_{i} \otimes m a_{j}) = (n \times m) (a_{i} \otimes a_{j})$	3) $\begin{matrix} [2 (a_{i}) \oplus (a_{j})] \equiv [(a_{i}) + (a_{i})] \oplus a_{j} \\ = [(a_{i} \oplus a_{j}) + (a_{i} \oplus a_{j})] \\ = 2 (a_{i} \oplus a_{j}) \end{matrix}$
4) transitive property if $[(a \otimes b), (b \otimes c)] \to [(a \otimes c)]$	4) transitive property if $[(a \otimes b), (b \otimes c), (a \otimes c)]$ if $[(a \oplus b), (b \oplus c)] \to [(a \oplus c)]$
5) $\begin{matrix} [(a_{i} \otimes a_{j}) \otimes a_{k}] = [(a_{i} \otimes a_{k}) \otimes a_{j}] \\ = [(a_{k} \otimes a_{j}) \otimes a_{i}] \end{matrix}$	5) $[(a_{i} \oplus a_{j}) \oplus a_{k}] = [(a_{i} \oplus a_{k}) \oplus (a_{j} \oplus a_{k})]$
$\underline{\otimes} \equiv [\otimes, \oplus]$ $\leftrightarrow$ composed operation
6) If ${[A = (a \oplus b)], [B = (c \oplus d)]}$ $\to$ $(A \underline{\otimes} B) = (a \oplus b) \otimes (c \oplus d)$
7) $(a \oplus b) \otimes (c \oplus d) = (a \otimes c) \oplus (a \otimes d) \oplus (b \otimes c) \oplus (b \otimes d)$
8) $[(a_{i} \otimes a_{j}) \oplus a_{k}] \neq [(a_{j} \otimes a_{i}) \oplus a_{k}] \leftrightarrow {(a_{i} \otimes a_{j})}_{\oplus} \neq {(a_{j} \otimes a_{i})}_{\oplus}$