$(20$ points$)$ Perceptron. Consider a parceptron training rule as described in class and class materials. Given an incorrectly classified point x in R d $,$ prove or disprove that a$)(10$ points$)$ the signed distance to the hyperplane increases upon the weight vector update if x is underclassified and that it decreases if x is overclassified. b$)(10$ points$)$ the absolute value of the signed distance decreases upon the weight vector update for any incorrectly classified x$.$