Fallacy of the undistributed middle

The fallacy of the undistributed middle occurs when the term that links the two premises is never distributed.

In this example, distribution is marked in boldface:

All Z is B
All Y is B
Therefore, all Y is Z
B is the common term between the two premises (the middle term) but is never distributed, so this syllogism is invalid. B would be distributed by introducing a premise which states either All B is Z, or No B is Z.

Also, a related rule of logic is that anything distributed in the conclusion must be distributed in at least one premise.

All Z is B
Some Y is Z
Therefore, all Y is B
The middle term—Z—is distributed, but Y is distributed in the conclusion and not in any premise, so this syllogism is invalid.