  The Tsetlin Machine (TM) is a novel machine-learning algorithm based on
propositional logic, which has obtained state-of-the-art performance on several
pattern recognition problems. In previous studies, the convergence properties
of TM for 1-bit operation and XOR operation have been analyzed. To make the
analyses for the basic digital operations complete, in this article, we analyze
the convergence when input training samples follow AND and OR operators
respectively. Our analyses reveal that the TM can converge almost surely to
reproduce AND and OR operators, which are learnt from training data over an
infinite time horizon. The analyses on AND and OR operators, together with the
previously analysed 1-bit and XOR operations, complete the convergence analyses
on basic operators in Boolean algebra.
