Discussion
A single layer perception cannot compute the following logical function :
Answer: C
A single layer perceptron cannot compute XOR.
A single layer perceptron computes a linear threshold function: it outputs 1 on one side of a straight line (a hyperplane) and 0 on the other. It can therefore represent only linearly separable functions.
AND, OR and NOT are linearly separable; for AND, for example, the line \(x_1 + x_2 = 1.5\) separates (1, 1) from the other inputs. XOR outputs 1 for (0, 1) and (1, 0) and 0 for (0, 0) and (1, 1), and no single straight line separates these two pairs. Minsky and Papert's analysis of this limitation is well known, and it is solved by adding a hidden layer.
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