Problem 2 let r be a relation on r defined as follows: for all x, y er, (x, y) r if and only
if ? > y?
(a) (8 points) is r reflexive, symmetric, antisymmetric, or transitive? for each of these ques-
tions, if the answer is positive, justify it as best you can; otherwise, give a counterexample.
(b) (2 points) is r a partial order relation? explain why.

An eight-sided die, which may or may not be a fair die, has four colors on it; you have been tossing the die for an hour and have recorded the color rolled for each toss. what is the probability you will roll a brown on your next toss of the die? express your answer as a simplified fraction or a decimal rounded to four decimal places.

Powerful women's group has claimed that men and women differ in attitudes about sexual discrimination. a group of 50 men (group 1) and 40 women (group 2) were asked if they thought sexual discrimination is a problem in the united states. of those sampled, 11 of the men and 19 of the women did believe that sexual discrimination is a problem. if the p-value turns out to be 0.035 (which is not the real value in this data set), then at = 0.05, you should fail to reject h0. at = 0.04, you should reject h0. at = 0.03, you should reject h0. none of these would be a correct statement.

In the diagram, gef and hef are congruent. what is the value of x