Step 1: Begin by understanding the processes of mitosis and meiosis. Mitosis is a type of cell division that results in two genetically identical daughter cells, while meiosis is a type of cell division that results in four genetically diverse haploid cells.
Step 2: Analyze the first option: 'involve the division of a parent cell's nucleus.' Both mitosis and meiosis involve nuclear division, so this statement is correct.
Step 3: Evaluate the second option: 'occur only in prokaryotic organisms.' Prokaryotic organisms do not undergo mitosis or meiosis because they lack a nucleus. Instead, they divide through binary fission. This statement is incorrect.
Step 4: Assess the third option: 'result in four haploid cells.' This is true for meiosis but not for mitosis, which produces two diploid cells. Therefore, this statement does not apply to both processes.
Step 5: Examine the fourth option: 'produce genetically identical daughter cells.' This is true for mitosis but not for meiosis, which produces genetically diverse cells. Thus, this statement does not apply to both processes.