Consider the dataset given below.

	a	b	c	d	e	f
x1	no	left	large	0	McDonalds	TRUE
x2	yes	left	medium	0	BurgerKing	TRUE
x3	yes	right	medium	1	Wendys	FALSE
x4	yes	right	small	1	Wendys	FALSE
x5	no	right	extraLarge	2	PizzaHut	FALSE

Using the Rule Induction from Coverings algorithm discussed in class, find each of the partitions specified below. (4 pts.)

{a}* =

{c}* =

{d}* =

{d, e}* =

Suppose that we are looking for a covering for decision attribute f which has partition {f}* = {{x1, x2}, {x3, x4, x5}}. (4 pts.)

Would {a}* work? Explain your answer.

Would {c}* work? Explain your answer.

Would {d}* work? Explain your answer.

Would {d, e}* work? Explain your answer.

Find a covering for f. If you found one in part b that worked, just use one of those. Using your covering, give a set of rules for decision attribute f. (1 pt.)