A term operation implication is introduced in a given basic algebra $𝒜$ and properties of the implication reduct of $𝒜$ are treated. We characterize such implication basic algebras and get congruence properties of the variety of these algebras. A term operation equivalence is introduced later and properties of this operation are described. It is shown how this operation is related with the induced partial order of $𝒜$ and, if this partial order is linear, the algebra $𝒜$ can be reconstructed by means of...