We have seen that a logistic regression model, which consists of a single artificial neuron with a sigmoid activation function, is unable to effectively solve the XOR dataset.

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Figure $2$: Some binary functions

$1.$ Let$$s demonstrate that the binary XOR function can be expressed as a combination of the binary AND, OR functions, along with negations.

$2.$ Create a Neural Network with $3$ neurons that implements the binary XOR function. Include a detailed description of the network, including the activation function, weights, and other relevant information.