The methods of agreement and difference are typically combined, both in everyday reasoning and in science. Mill called this combination the joint method of agreement and difference.

Why it is valuable to combine the methods of agreement and difference? The method of agreement, by itself, provides evidence that a is sufficient for E. Since the effect can occur in the absence of any other factor, none of the other factors is necessary, so we have reason to think that a is sufficient.

To tell whether a is necessary, we need to see whether the effect can occur in its absence--and that is what the method of difference tells us.

Thus, the methods of agreement and difference have complementary strengths. If we are trying to show that a is necessary and sufficient for E, we need to use the methods in combination.