e/Semigroup with two elements

Information
has gloss	eng: In mathematics, a semigroup with two elements is a semigroup for which the cardinality of the underlying set is two. There are exactly five distinct nonisomorphic semigroups having two elements: * O2, the null semigroup of order two, * LO2 and RO2, the left zero semigroup of order two and right zero semigroup of order two, respectively, * (0,1}, ∧) (where "∧" is the logical connective "and"), the non-null semigroup with zero of order two, * (Z2, +2) (where Z2 = 0,1} and "+2" is "addition modulo 2"): the group of order two. The semigroups LO2 and RO2 are antiisomorphic. O2, and are commutative, LO2 and RO2 are noncommutative. LO2, RO2 and are bands and also inverse semigroups.
lexicalization	eng: Semigroup with two elements
instance of	e/Algebraic structure