3: {20 points} Let A be a new-emptyr set and E=2"'_ Defute the following relation R in E: X R Y if K E Y a) Prove tltat R is a partial order. b) Is R a total order? For the test of the prohlc, assume n={s,b,c}. c) Draw the graph of R and tlte Hess diagram of R in E. d) Docs E have a maximum? If so, what is it? cl Docs E have a minimum? lf'so, what is it? 1] Let F= E-{tit, A}. If F has a maximtun, give its maximum; otherwise, give the maximals of F. Also, if F has a minimtun, give its minimum; otherwise, give the minimals of F \"it: Den a relation is dened by combining two {or more] conditions with logical connectives {\"and\" and \"or"]_ For example, a \"mote-useful\" relation between cars can be dened as: x is more useful than 3; it' x is bigger an_d strongr than 5:. Another example, this time of a relation between cars ofthe same model is: x is worse than 3 ifx is Mot w more mileage than 3;. In such situations, it is better to determine the properties of each condition W (Le, as a separate relation) and see how the properties of combined relations combine together. The next two problems are about that