Let T denote a set of training examples, each of the form (\textbf{x},y) = (x_1, x_2, x_3, .., x_k, y) where x_a\in vals(a) is the value of the ath attribute of example \textbf{x} and y is the corresponding class label.
The mutual information is equal to the total entropy for an attribute if for each of the attribute values a unique classification can be made for the result attribute.