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Given U = {x | x∈Z, 5≤x≤20} and its three subsets: A = { a | a∈U, a is even}, B = { b | b∈U, b≤10} ,
C = { c │c∈U, c>8 }. Find A∩BUC.
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- 11. (See Exercise 10.) According to Definition 5.29, is defined in by if and only if . Show that if and only if . 10. An ordered field is an ordered integral domain that is also a field. In the quotient field of an ordered integral domain define by . Prove that is a set of positive elements for and hence, that is an ordered field. Definition 5.29 Greater than Let be an ordered integral domain with as the set of positive elements. The relation greater than, denoted by is defined on elements and of by if and only if . The symbol is read “greater than.” Similarly, is read “less than.” We define if and only if. As direct consequences of the definition, we have if and only if and if and only if . The three properties of in definition 5.28 translate at once into the following properties of in . If and then . If and then . For each one and only one of the following statements is true: . The other basic properties of are stated in the next theorem. We prove the first two and leave the proofs of the others as exercises.Two HR managers ranked the 12 entries to hire executives for operations department of a hospital is as follows. What degree of agreement is there between the judges? HR Manager 1 1 2 3 4 5 6 7 8 9 10 11 12 HR Manager 2 12 9 6 10 3 5 4 7 8 2 11 1Two persons participated in five shooting competition and were able to hit the targetcorrectly out of fifteen shots as given below.Competitor A 6 12 12 10 7Competitor B 12 15 7 7 4Which competitor is more uniform in shooting performance?
- A sample space has 3 outcomes, {1,2,3}{O1,O2,O3}. Suppose E={1,2}E={O1,O2}, and F={1,3}F={O1,O3}. If Pr[E]=0.61Pr[E]=0.61 and Pr[F]=0.6Pr[F]=0.6, what is Pr[{2,3}]Pr[{O2,O3}]? lines are just qsA survey asked 816 college freshmen whether they had been to a movie or eaten in a restaurant during the past week. Thefollowing information was obtained: 393 freshmen had been to neither a movie nor a restaurant, and 265 had been to amovie. If 90 of those who had been to a movie had not been to a restaurant, how many of the surveyed freshmen had been tothe following?(a) both a movie and a restaurant (b) a movie or a restaurant (c) a restaurant (d) a restaurant but not a movieGiven that p(A)=.52, and p(A│B)=.89, are A and B (a) independent? (b) exclusive?
- Applying the Venn Diagram, A teacher announces that out of 30 students in class, 16 passed both Math and Science tests, and 24 passed the Science test. How many passed students did not passed either Math or Science test?Given that p(A)=.31, p(B│A) =.39, and p(A│B) =.31, are A and B (a) independent? (b) exclusive?Although consumers often want to touch products before purchasing them, they generally prefer that others have not touched products they would like to buy. Can another person touching a product create a positive reaction? Subjects were given instructions to contact a sales associate at a university bookstore who would provide them with a shirt to try on. When meeting the sales associate, subjects were told that there was only one shirt left and it was being tried on by another “customer.” The other customer trying on the shirt was a confederate of the experimenter and was either an attractive, well-dressed professional female model or an average-looking female college student wearing jeans and a tee shirt. Subjects, who were either males or females, saw the confederate leaving the dressing room, where the shirt was left for them to try on. There was also a control group of subjects who were handed the shirt directly off the rack by the sales associate. Thus, there were five treatments:…
