Final answer:
The president's inaction resulting in a bill's rejection due to Congress adjourning within ten days is known as a pocket veto. It prevents the bill from becoming law without the need for a formal veto and cannot be overridden by Congress.
Step-by-step explanation:
If the president does not act on a bill sent to him by Congress, and instead allows the bill to be rejected by default because Congress will adjourn in less than ten days, this is referred to as a pocket veto.
During the legislative process, the President has several options regarding a bill passed by Congress. If the President approves the bill, he can sign it into law. If the President disapproves, he can veto the bill and return it to Congress with his objections for reconsideration. If two-thirds of both the House and Senate vote to pass the bill after a presidential veto, it overrides the veto and becomes law. However, if the President takes no action and Congress adjourns within ten days (excluding Sundays) of sending the bill to the President, the bill does not become law and is considered to be pocket vetoed.
Unlike a regular veto, a pocket veto cannot be overridden because Congress is not in session to reconsider the bill. This makes the pocket veto a definitive legislative action by the President to prevent a bill from becoming law without his formal signature or veto message.