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Prove the domination laws in Table 1 by showing thata) A ?

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

Solution for problem 7E 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

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Problem 7E

Prove the domination laws in Table 1 by showing that

a) A ∪ U = U.

b) A ∩ ∅ = ∅.

Step-by-Step Solution:
Step 1 of 3

Step-1:

   

 NOTE: A set A is a subset of a set B  , or equivalently  B is  a superset of A , if A is contained inside B, that is all elements of A are also elements of B. A and B may coincide.That is

                                               

    UNION: The union of  two  sets  A and B  is  the  set containing  all elements that are in A  or in B ( possibly both).

       Then it is denoted by    , we can write  if and only if  or .

       Note :

     Example :

          A= { a, b} , B = {b ,c} then .

   The union of sets A and B is  shown by the shaded area in the venn diagram:

                                       

                 

Step-2:                                      

  a)In this problem we need to show that .

     Consider ,  .

      By the definition of union   (or)  .

      We know that   is a universal set .So ,   .

      Therefore ,   .

       ………….(1)

From the definition of the subset and union we get …………(2)

Therefore...

Step 2 of 3

Chapter 2.2, Problem 7E is Solved
Step 3 of 3

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

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Prove the domination laws in Table 1 by showing thata) A ?

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