1) The following real dataset contains information about two different flowers: Iris setosa and Iris versicolor. 

Species	Sepal length	Sepalwidth	Petal length	Petal width
Iris setosa	4.9	3.0	1.4	0.2
Iris versicolor	5.6	2.5	3.9	1.1

a)      What is the supremum distance between these two objects?
b)     Compute the Minkowski distance between these two objects, using p = 3.
2)     The following real dataset contains two samples from the dataset for Prediction of Molecular Bioactivity for Drug Design – Binding to Thrombin, with sampled features. For each activity (F1, F2, …, F10), the class value (0/1) indicates if the activity is active or inactive.

Cases	F1	F2	F3	F4	F5	F6	F7	F8	F9	F10
1	0	1	1	0	0	0	1	1	1	1
2	0	1	0	0	1	0	1	0	0	1

Assume all the activities are asymmetric binary variables. What is the Jaccard coefficient between case 1 and case 2?
3)    The following real world dataset contains two samples from Car Evaluation Database . The model evaluates cars according to the following concept structure:

CAR	car acceptability
.PRICE	overall price
. . buying	buying price
. . maint	price of the maintenance
. TECH	technical characteristics
. . COMFORT	comfort
. . . doors	number of doors
. . . persons	capacity in terms of persons to carry
. . . lug_boot	the size of luggage boot
. . safety	estimated

The attribute values are as follows:

Attribute	Values (categorical)
buying	v-high, high, med, low
maint	v-high, high, med, low
doors	2, 3, 4, 5 - more
persons	2, 4, more
lug_boot	small, med, big
safety	low, med, high

Now, assume we use simple match to estimate the proximity between objects. What is the distance between Car 1 and Car 2? 

Case

buying

maint

doors

persons