2.1Minsky和Papert指出：感知機因為是線性模型，所以不能表示複雜的函式，如異或。驗證感知機為什麼不能表示異或

明顯可知異或不具有線性可分性，由感知機定義可知，感知機不能表示異或。

2.2模仿例題2.1，構建從訓練資料集求感知機模型的例子

import numpy as np  
import matplotlib.pyplot as plt  

class showPicture:  
    def __init__(self,data,w,b):  
        self.b = b  
        self.w = w  
        plt.figure(1)  
        plt.title('Plot 1', size=14)  
        plt.xlabel('x-axis', size=14)  
        plt.ylabel('y-axis', size=14)  

        xData = np.linspace(0, 5, 100)  
        yData = self.expression(xData)  
        plt.plot(xData, yData, color='r', label='y1 data')  

        plt.scatter(data[0][0],data[0][1],s=50)  
        plt.scatter(data[1][0],data[1][1],s=50)  
        plt.scatter(data[2][0],data[2][1],marker='x',s=50,)  
        plt.savefig('2d.png',dpi=75)  
    def expression(self,x):  
        y = (-self.b - self.w[0]*x)/self.w[1]  
        return y  
    def show(self):  
        plt.show()  
class perceptron:  
    def __init__(self,x,y,a=1):  
        self.x = x  
        self.y = y  
        self.w = np.zeros((x.shape[1],1))  
        self.b = 0  
        self.a = 1  
    def sign(self,w,b,x):  
        result = 0  
        y = np.dot(x,w)+b  
        return int(y)  
    def train(self):  
        flag = True  
        length = len(self.x)  
        while flag:  
            count = 0  
            for i in range(length):  
                tmpY = self.sign(self.w,self.b,self.x[i,:])  
                if tmpY*self.y[i]<=0:  
                    tmp = self.y[i]*self.a*self.x[i,:]  
                    tmp = tmp.reshape(self.w.shape)  
                    self.w = tmp +self.w  
                    self.b = self.b + self.y[i]  
                    count +=1  
            if count == 0:  
                flag = False  
        return self.w,self.b   
 

2.3證明：樣本集線性可分的充要條件是正例項點集所構成的凸殼和負例項點集構成的凸殼不相交