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Without using Venn diagrams, write (A' UNION B)' INTERSECT A' in its simplest form.

Without using Venn diagrams, write (A' UNION B)' INTERSECT A' in its simplest form.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Without using Venn diagrams, write (A' UNION B)' INTERSECT A' in its simplest form.
Note: each rule used must be included with each step.

Expert Solution
Definitions:

Definitions:   (a)  A∪B={x/x∈A or x∈B}

                     (b)  A∩B={x/x∈A  and  x∈B}

                     (c)  If  A ⊂ B  and B ⊂ A ⇒ A = B

                     (d)   A ⊂ B  if and only if every element in A is an element in B.

Now we will show that   A∪B∩A=A by using above definitions.

 

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