Which of the following actions can lead to a partnership being considered null and void?

A partnership is generally defined as an association of two or more persons to carry on a business for profit. The critical element that distinguishes a partnership from other forms of business association is the profit motive. If a partnership lacks a profit motive, it fundamentally fails to meet this essential criterion, which can lead to it being considered null and void.

In examining the other choices, each of them does not inherently negate the existence of a partnership. The presence of an oral agreement (regardless of whether it's formalized in writing) does not invalidate a partnership, as partnerships can be formed through oral or informal agreements, provided the necessary elements exist. Similarly, operating under a single business name is a common practice among partnerships and does not affect their legal status. Lastly, the familial relationship among partners does not invalidate the partnership; partners can legally be relatives and still form a valid partnership as long as they meet the other legal criteria.

Thus, the absence of a profit motive fundamentally disrupts the very nature of what constitutes a partnership, making that the correct answer.