A pure subset in a decision tree is 1 A subset with similar values of target variable A subset with 50:50 values of target variable A subset with a mix of values of target variable A subset with one prediction

Q1 Classification The classification tree was trained with response data Y and using two explanatory variables X1, X2. Yes X20.310283 X10.606056 No X2 0.697338 Yes Yes ## A) Sketch the classification implied by the tree in the region [0,1] 2. Use "Yes" /1 and "No"/0. B) A new set of points has been provided with fresh response values, as follows. x1 x2 Y ## [1,] 0.25 0.33 1 ## [2,] 0.50 0.33 0 ## [3,] 0.75 0.33 0 ## [4,] 0.25 0.67 0 ## [5,] 0.50 0.67 0 ## [6,] 0.75 0.67 1 Using the data and the trained tree, give predicted (0/1) labels for the new points. C) Report the confusion matrix and performance measures TPR=| on the performance of this classifier. and FPR= Briefly comment D) Can the given trained tree be trimmed to a simpler version, removing redundancies? E) Write a different tree that is equivalent to the given one.

Draw syntactic trees for the following two sentences and apply the Hobbs tree-search algorithm to it for the pronoun “his”, showing each step in the search: Alan Smithee, a prolific movie director, has over 50 movies to his name, although he is considered one of the worst directors of all time. For over 50 years, he has delivered substandard films to the big screen.

Use truth trees to determine whether the following symbolized arguments are valid or invalid. 1. P~N II NvP 2. ~(G&M), Mv~G II ~G 3. K~L, ~L&~K II K->L 4. Z II E->(Z->E) (For some reason, students find this one difficult. "Z" is the premise. Don't be fooled. This IS a tree that does not branch. It is a stalk, a demon stalk. 5. CD, Ev-D II E->C 6. A(BvC), ~CvB II A->B 7. J-> (K->L), K->(J->L) II (JvK)->L 8. -(KS), S->~(RvK) II Rv~S 9. E->(F&G), F->(G->H) II E->H .0. A->(NvQ), ~(Nv~A) II A->Q