4.Suppose the universe is the set of all living human beings, are the following relations transitive? are they reflexive? and are they symmetric?

(10points)

a.is married to

b.is friends with

c.lives on the same floor as

d.detests

e.is the sister of

5.The PH Corporation is introducing a new line of portable computers. Version has long battery life but is not very slim. Version is extremely slim but does not have a long battery life.

(a)Draw a graph with battery life on the x-axis and slimness on the y-axis. Clearly dot the location of and .

(3points)

(b)Market research suggests that a typical consumer tends to be indifferent between and . Using solid lines, represent a typical consumer's indifference curves going through and .

(2points)

(c)PH wants to steer customers toward the slightly more profitable version . They decide to use a decoy, which they will call , to accomplish this goal. On your graph, shade the region where a suitable decoy could be placed.

(3points)

(d)Assuming the decoy works as anticipated, use a dashed line to show what the typical consumer's indifference curves would look like after the introduction of the .

(2points)