Boolean algebra is the finitary algebra of two values. It resembles the algebra of real numbers as taught in high school, but with the numeric operations of multiplication xy, addition x + y, and negation −x replaced by the logical operations of conjunction x∧y, disjunction x∨y, and complement ¬x. The Boolean operations are these and all other operations obtainable from them by composition; equivalently, the finitary operations on the set {0,1}. The laws of Boolean algebra can be defined axiomatically as the equations derivable from a sufficient finite subset of those laws, such as the equations axiomatizing a complemented distributive lattice or a Boolean ring, or semantically as those equations identically true or valid over {0,1}. The axiomatic approach is sound and complete in the sense that it proves respectively neither more nor fewer laws than the validity-based semantic approach.