Which Boolean operation outputs true if at least one input is true?

The Boolean operation that outputs true if at least one input is true is the OR operation. In Boolean logic, the OR operator evaluates to true if either or both of its operands are true. For example, if you have two conditions, A and B, the expression A OR B results in true if A is true, B is true, or both A and B are true. This characteristic makes the OR operation essential in scenarios where a positive outcome is desired from multiple possible true conditions.

In contrast, the AND operation requires all inputs to be true for the output to be true. The XOR (exclusive OR) operation outputs true only if one, and not both, of the inputs is true, which is more restrictive. Lastly, the NAND operation outputs false only when all inputs are true, making it the opposite of the AND operation. Therefore, the OR operation is the only one among the choices that satisfies the condition of outputting true with at least one true input.