Perceptron exercise

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I wonder how to find a solution to the following questions:

Q: Design a two-input perceptron that implements the boolean function A ∧¬ B?

Q: Design a two-layer network of perceptrons that implements A XOR B.

Q: If it's possible to design one-layer perceptron that implements A XOR B?

What is the general approach to solve the exercise. The asnwer can be found in solutions.

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The general approach is the back-propagation algorithm, but for simple cases like yours you can work out the right weights by searching through a small subset of the possible values and come up with a rough approximation of the best weights.