1. (30 pts) Recall from Boolean algebra that there are2216 different binary Boolean functions including AND, OR, NOT and XOR. Show that XOR and XOR are the only two binary Boolean functions among all the 16 Boolean functions that cannot be implemented with or learned by a perceptron as defined in lecture. You may approach this problem in two ways: 1) Prove that a binary Boolean function f(x?, X2) is implementable with a perceptron if and only if any of the following Boolean functions is implementable with a perceptron: f(x1, X2), f(X1, X2), f(x1%), fFor ). Then use the facts that AND, OR, and NOT are implementable while XOR is not implementable with single perceptrons to draw your conclusion. 2) Prove that XOR is not implementable with a perceptron and for each binary Boolean function except AND, OR, NOT, XOR and XOR, give the linear combination of the two inputs (i.e., Wo, W and W2) for the perceptrorn that implement the Boolean function. You may assume that the activation function is a threshold function with the threshold being 0 1. (30 pts) Recall from Boolean algebra that there are2216 different binary Boolean functions including AND, OR, NOT and XOR. Show that XOR and XOR are the only two binary Boolean functions among all the 16 Boolean functions that cannot be implemented with or learned by a perceptron as defined in lecture. You may approach this problem in two ways: 1) Prove that a binary Boolean function f(x?, X2) is implementable with a perceptron if and only if any of the following Boolean functions is implementable with a perceptron: f(x1, X2), f(X1, X2), f(x1%), fFor ). Then use the facts that AND, OR, and NOT are implementable while XOR is not implementable with single perceptrons to draw your conclusion. 2) Prove that XOR is not implementable with a perceptron and for each binary Boolean function except AND, OR, NOT, XOR and XOR, give the linear combination of the two inputs (i.e., Wo, W and W2) for the perceptrorn that implement the Boolean function. You may assume that the activation function is a threshold function with the threshold being 0