Boolean algebra

a) An algebra in which all elements can take only one of two values (typically 0 and 1, or "true" and "false") and are subject to operations based on AND, OR and NOT

The set of divisors of 30, with binary operators: g.c.d. and l.c.m., unary operator: division into 30, and identity elements: 1 and 30, forms a Boolean algebra.

b) An algebra with two binary operators which are both associative, both commutative, such that both operators are distributive with respect to each other, with a pair of identity elements: one for each operator, and a unary complementation operator which simultaneously yields the inverse with respect to both operators.

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