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Prove the second associative law from Table 1 by showing

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen ISBN: 9780073383095 37

Solution for problem 22E Chapter 2.2

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

Discrete Mathematics and Its Applications | 7th Edition

4 5 0 321 Reviews
29
1
Problem 22E

Prove the second associative law from Table 1 by showing that if A,b. and C are sets, then A ∩ (b ∩ C) = (A ∩ B) ∩ C

Step-by-Step Solution:

Step 1:

Consider the three sets A and b and C we have to prove that            

 

Which is  associative law of sets for union

Step 2:

Definition:

(1)Let A and B are two sets then then two sets A and B are said to be equal if these two sets are subset of each other that is A=B if and

(2)

Step 3:

Here we prove that L.H.S(left hand side) is subset of  R.H.S(left hand side) and R.H.S(left hand side) is subset of  L.H.S(left hand side)

Consider L.H.S,

Let then by definition

Then again by definition,

Thus if  then  

    …(1)

Step 4 of 5

Chapter 2.2, Problem 22E is Solved
Step 5 of 5

Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095. This full solution covers the following key subjects: associative, Law, prove, Sets, showing. This expansive textbook survival guide covers 101 chapters, and 4221 solutions. The answer to “Prove the second associative law from Table 1 by showing that if A,b. and C are sets, then A ? (b ? C) = (A ? B) ? C” is broken down into a number of easy to follow steps, and 29 words. Since the solution to 22E from 2.2 chapter was answered, more than 435 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7. The full step-by-step solution to problem: 22E from chapter: 2.2 was answered by , our top Math solution expert on 06/21/17, 07:45AM.

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