Prove the identity 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 6E Chapter 2.2

Discrete Mathematics and Its Applications | 7th Edition

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Problem 6E

Prove the identity laws in Table 1 by showing that

a) A ∪ ∅ = A.

b) A ∩ U = 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 $A⊆\ B$

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 $A\cup{}B$ , we can write $x\epsilon{}\ (A\cup{}B)$ if and only if $x\epsilon{}A$ or $x\epsilon{}B$ .

Note : $A\cup{}B\ =\ B\cup{}A$

Example :

A= { a, b} , B = {b ,c} then $A\cup{}B\ =\ \ \{a\ ,\ b,\ c\}$ .

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 $A\cup{}\varphi{}\ =\ A$ .

Consider , $a\ \epsilon{}\ A\cup{}\varphi{}$ .

By the definition of union $a\ \epsilon{}A$ (or) $a\ \epsilon{}\ \varphi{}$ .

We know that $\varphi{}$ is a null set .So , $a\notin{}\varphi{}$ .

Therefore , $a\ \epsilon{}\ A$ ...

Step 2 of 3

Chapter 2.2, Problem 6E is Solved

Step 3 of 3

Textbook: Discrete Mathematics and Its Applications

Edition: 7

Author: Kenneth Rosen

ISBN: 9780073383095

The full step-by-step solution to problem: 6E from chapter: 2.2 was answered by , our top Math solution expert on 06/21/17, 07:45AM. This full solution covers the following key subjects: Identity, laws, prove, showing, Table. This expansive textbook survival guide covers 101 chapters, and 4221 solutions. The answer to “Prove the identity laws in Table 1 by showing thata) A ? ? = A.________________b) A ? U = A.” is broken down into a number of easy to follow steps, and 20 words. Since the solution to 6E from 2.2 chapter was answered, more than 304 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. Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095.