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A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![15.
Prove the Absorption Laws: (a) AU(AN B) = A;
AN(AUB) = A.
16.
Mahnrago
Let S = {1, 2, ., 8, 9}. Determine whether or not each of the following is a partition of S:
(a) [{1, 3, 6}, (2, 8), (5, 7,9}]
(c) [{2, 4, 5, 8). (1, 9). (3, 6, 7}]
(b) [{1, 5, 7), (2, 4, 8, 9), {3, 5, 6}] (d) [{1, 2, 7}, {3, 5}, (4, 6, 8, 9}, (3, 5}]
17.
Let S = {1, 2, 3, 4, 5, 6}. Determine whether or not each of the following is a partition of S:
(a) Pi = [{1, 2, 3}. (1, 4, 5, 6}]
(b) P2 [{1, 2}, (3, 5, 6}]
(c) P3 = [{1, 3, 5}. (2, 4}, {6}]
(d) P4 = [{1, 3, 5), (2, 4, 6, 7}]
18.
Let S = (1, 2, 3, .., 8, 9}. Find the cross partition P of the following partitions of S:
P1 = [{1, 3, 5, 7, 9}, {2, 4, 6, 8}] and P2 = [{1, 2, 3, 4}. (5, 7}, (6, 8, 9}]
15](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd0ef77e0-0e9b-4019-9449-4a94b2c49a97%2F4d63b93b-644b-49dd-95bb-d79e4f1b4024%2Fpoabhyn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:15.
Prove the Absorption Laws: (a) AU(AN B) = A;
AN(AUB) = A.
16.
Mahnrago
Let S = {1, 2, ., 8, 9}. Determine whether or not each of the following is a partition of S:
(a) [{1, 3, 6}, (2, 8), (5, 7,9}]
(c) [{2, 4, 5, 8). (1, 9). (3, 6, 7}]
(b) [{1, 5, 7), (2, 4, 8, 9), {3, 5, 6}] (d) [{1, 2, 7}, {3, 5}, (4, 6, 8, 9}, (3, 5}]
17.
Let S = {1, 2, 3, 4, 5, 6}. Determine whether or not each of the following is a partition of S:
(a) Pi = [{1, 2, 3}. (1, 4, 5, 6}]
(b) P2 [{1, 2}, (3, 5, 6}]
(c) P3 = [{1, 3, 5}. (2, 4}, {6}]
(d) P4 = [{1, 3, 5), (2, 4, 6, 7}]
18.
Let S = (1, 2, 3, .., 8, 9}. Find the cross partition P of the following partitions of S:
P1 = [{1, 3, 5, 7, 9}, {2, 4, 6, 8}] and P2 = [{1, 2, 3, 4}. (5, 7}, (6, 8, 9}]
15
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