Let us assume neuron which aggregates the input and makes a decision on the basis of this aggregation. If sum of all inputs is greater than the given threshold 𝚹 then output of this neuron is 1 else it is 0. We can implement a boolean function with this neuron if output of this neuron is consistent with the truth table of the boolean function. In other words if the given input configuration for the boolean function outputs 1 then neuron should also give 1 to the same configuration. Consider the following boolean function (x1 And x2) AND (!x3 And !x4) The neuron is depicted in the following figure
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