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A NAND gate is a digital logic gate that outputs false only when all its inputs are true. In other words, the output of a NAND gate is true in every other scenario except when every input is high.

When both inputs are on (true), the NAND gate's output becomes false. In all other cases—at least one input is false (off)—the output will be true. This is why understanding the function of the NAND gate is fundamental in logic design and circuits: it primarily serves to provide a negation of the AND operation.

In the context of the other choices, if one input is on without the other, or if both inputs are off, the output remains true. This demonstrates that the NAND gate's defining characteristic is its unique response to having both inputs active simultaneously.