Which logical operation cannot be represented by a simple perceptron?

A simple perceptron is a type of artificial neuron that applies a linear transformation to its inputs and produces a binary output based on whether the weighted sum exceeds a certain threshold. It can effectively represent logical operations that are linearly separable. The operations such as AND and OR can be represented by a simple perceptron because they can be plotted as points on a graph that can be separated by a straight line.

The NOT operation can also be represented by a perceptron by using a single input; it essentially inverts the input value. However, the XOR operation is unique because it requires a nonlinear separation of inputs. The XOR logic gate outputs true only when the inputs differ (i.e., one is true and the other is false). Representing this operation requires a more complex network structure (multilayer perceptron) since a single line cannot divide the true outputs from the false ones in the input space.

Thus, the XOR function cannot be implemented with a simple perceptron, making it the correct answer to this question.