The statement is a bit misleading. All living cells, including bacteria, contain hereditary material. This material is typically organized into DNA, though some viruses use RNA instead.

Here's why the statement might be phrased that way:

* Eukaryotic cells have a nucleus: Eukaryotic cells (like those in plants, animals, fungi, and protists) have a distinct nucleus where their DNA is housed.

* Bacteria are prokaryotes: Bacteria (and archaea) are prokaryotic, meaning they lack a nucleus. Their DNA is located in a region called the nucleoid, which isn't enclosed by a membrane.

So, while bacteria don't have a nucleus that contains their hereditary material, they absolutely have DNA, which is their genetic blueprint.

Let me know if you have any other questions!