Final answer:
When the sole proprietor of a business invests more cash in it, the assets increase, liabilities remain the same, and owners' equity increases.
Step-by-step explanation:
When the sole proprietor of a business invests more cash in it, the fundamental accounting equation is affected in the following way:
Assets increase, as cash, which is an asset, is being invested in the business.
Liabilities remain the same, as there is no change in the amount owed by the business to creditors.
Owners' equity increases, as the additional cash investment by the sole proprietor increases their ownership stake in the business.
Therefore, the correct answer is option 4) assets increase, liabilities remain the same, and owners' equity increases.