AU (Bn C))° = (c U Bº)n A°
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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is this true or false? use indirect or direct method to prove
discrete math
![The image displays a mathematical expression involving set operations and complements. The expression is:
\[
(A \cup (B \cap C))^c = (C^c \cup B^c) \cap A^c
\]
This equation demonstrates one of De Morgan's Laws, which relates the complement of unions and intersections of sets. Here's a breakdown of the components:
- \(A, B, C\) are sets.
- \(\cup\) represents the union of sets, meaning all elements that are in either set.
- \(\cap\) represents the intersection of sets, meaning all elements that are in both sets.
- The superscript \(c\) indicates the complement of a set, meaning all elements not in the set.
According to De Morgan's Law, the complement of a union is the intersection of the complements, and vice versa. This equation specifically shows how to distribute the complement over a union and an intersection.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8e824278-0cf8-4697-a6ac-3768c642cb77%2F2553e236-0573-40b9-9d5c-f341d1729302%2Feqs8av9_processed.png&w=3840&q=75)
Transcribed Image Text:The image displays a mathematical expression involving set operations and complements. The expression is:
\[
(A \cup (B \cap C))^c = (C^c \cup B^c) \cap A^c
\]
This equation demonstrates one of De Morgan's Laws, which relates the complement of unions and intersections of sets. Here's a breakdown of the components:
- \(A, B, C\) are sets.
- \(\cup\) represents the union of sets, meaning all elements that are in either set.
- \(\cap\) represents the intersection of sets, meaning all elements that are in both sets.
- The superscript \(c\) indicates the complement of a set, meaning all elements not in the set.
According to De Morgan's Law, the complement of a union is the intersection of the complements, and vice versa. This equation specifically shows how to distribute the complement over a union and an intersection.
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