1. Let A and B be two finite sets such that nA) - 20, n(B) - 28 and niA u B) -36, find nlA n BJ.a. 10b. 11c. 12d. 142. If n[A - B) - 18, nțA u B) - 70 and nțA N B) - 25, then find n[B).e. 52d. 60a. 50b. 483. In a group of 60 people, 27 like cold drinks and 42 like hot drinks and eachperson likes at least one of the two drinks. How many like both coffee andtea?a. 9 people like both tea and coffeeb. 12 people like hoth tea and coffeec. 13 people like both tea and coffeed. 14 people like both tea and coffee4. In a class of 60 students, 40 students like math, 36 like science, 24 like boththe subjects. Find the number of students who like (i) Math only (ii) Scienceonly (i) Either Math or Science (IV) Neither Math nor science.a. ) 16. (i) 12, (i) 52 and (iv) 8b. ( 17. (i) 13, (i) 45 and (iv) 10c. ( 16, (i) 14 , ) 50 and (iv) 8d. ) 15, (i) 14 . (ii) 20 and (iv) 8

As per bartleby guidelines, I need to answer only one question. But, I had answered the first two…

Answered: 1. Let A and B be two finite sets such…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.4: Ordered Integral Domains

Problem 11E: 11. (See Exercise 10.) According to Definition 5.29, is defined in by if and only if . Show that ...

See similar textbooks

Similar questions

Prove or disprove that AB=AC implies B=C.
For the sets given in Exercise 9, is there a distributive relationship for intersection with respect to union? That is, does ABC=ABAC? A=1,2,3,4, B=2,4,6,8, and C=1,3,5,7,9.
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.
For the sets gives in Exercise 9, is there a distributive relationship for union with respect with respect in intersection? That is does ABC=ABAC? A=1,2,3,4, B=2,4,6,8, and C=1,3,5,7,9.
Is the set named empty, finite, or infinite? a N=countingnumbers b V=vowels c P=pointsintheintersectionoftwodisjointsets
Prove that if , , and , then .

Recommended textbooks for you

Elements Of Modern Algebra

Algebra

ISBN:

9781285463230

Author:

Gilbert, Linda, Jimmie

Publisher:

Cengage Learning,

Elementary Geometry For College Students, 7e

Geometry

ISBN:

9781337614085

Author:

Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:

Cengage,

Elements Of Modern Algebra

Algebra

ISBN:

9781285463230

Author:

Gilbert, Linda, Jimmie

Publisher:

Cengage Learning,

Elementary Geometry For College Students, 7e

Geometry

ISBN:

9781337614085

Author:

Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:

Cengage,

SEE MORE TEXTBOOKS

1. Let A and B be two finite sets such that n(A) - 20, n(B) - 28 and njA u B) 36, find nțA n B). а. 10 b. 11 e. 12 d. 14 2. If n[A - B) - 18, nlA U B) - 70 and njA N B) - 25, then find n[B). a. 50 b. 48 e. 52 d. 60