Which logic gate outputs false only when both inputs are false?

The output behavior of the OR gate is such that it outputs true (or high) when at least one of its inputs is true. Therefore, it will only output false (or low) when both inputs are false. This characteristic aligns perfectly with the description given in the question: it outputs false only under the condition that both inputs are false.

In contrast, the NOR gate outputs true only when both inputs are false, which does not fit the requirement of the question as it does not output false specifically when both inputs are false. The AND gate requires that both inputs be true to output true, hence it produces false whenever either input is false, but that does not specifically match the criterion of outputting false only when both inputs are false. The XOR gate outputs true when the inputs are different and false when both inputs are the same, meaning it can output false under differing conditions than specified in the question.

Thus, the OR gate is the appropriate choice since it directly satisfies the condition of outputting false solely when both inputs are false.