Final answer:
The statement is true; the nucleus of a eukaryotic cell directs its activities and contains its DNA, acting as the control center and storing genetic instructions for protein synthesis.
Step-by-step explanation:
The statement, "The nucleus is the part of a eukaryotic cell that directs cell activities and contains genetic information stored in DNA," is true. The nucleus is the command center of the cell, housing most of the cell's genetic material (DNA).
This genetic material provides the instructions necessary for the cell's functioning, encompassing the synthesis of molecules required for life. Enclosed by the nuclear envelope, a double lipid bilayer, the nucleus regulates the influx and outflow of substances through nuclear pores.
The nucleus is also the site where DNA is organized into chromatin and chromosomes, and it controls gene expression, the process through which DNA is used to create proteins. Despite its importance, some cells, like muscle cells, can have multiple nuclei, while others, such as mammalian red blood cells, have none because they remove their nuclei during maturation.