1. Consider a spam detection task using with 5 attributes, x1 through x5, representing whether or not 5 spammy words are present: Congratulations, Important, Reward, Offer, and Free. Suppose you wish to label any message as spam if it has at least 3 of these 5 words, or (equivalently) if at least 3 of the attributes x1, . . . , x5 are equal to 1.

(a) Draw a decision tree that represents this decision function.

(b) Specify the weights and bias of a linear model that represents this decision function.

(c) Construct a small dataset so that 1-nearest neighbor would make predictions matching this decision function.