Select the law that establishes that the two sets below are equal: Gn (GU Z) = G OAbsorption Law O Domination Law O De Morgan's Law O Idempotent Law
Select the law that establishes that the two sets below are equal: Gn (GU Z) = G OAbsorption Law O Domination Law O De Morgan's Law O Idempotent Law
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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![**Question:**
Select the law that establishes that the two sets below are equal:
\[ G \cap (G \cup Z) = G \]
**Options:**
- Absorption Law
- Domination Law
- De Morgan's Law
- Idempotent Law
**Explanation:**
The given expression \( G \cap (G \cup Z) = G \) is an example of the Absorption Law. The Absorption Law in set theory states that:
\[ A \cap (A \cup B) = A \]
This law demonstrates that if you take the intersection of a set with the union of itself and another set, you will end up with the original set.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf74fb9e-b533-4057-a79c-37c4b56e1189%2F85eab7ee-f0e2-468f-bfc5-9dd067271242%2Ff324c7b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
Select the law that establishes that the two sets below are equal:
\[ G \cap (G \cup Z) = G \]
**Options:**
- Absorption Law
- Domination Law
- De Morgan's Law
- Idempotent Law
**Explanation:**
The given expression \( G \cap (G \cup Z) = G \) is an example of the Absorption Law. The Absorption Law in set theory states that:
\[ A \cap (A \cup B) = A \]
This law demonstrates that if you take the intersection of a set with the union of itself and another set, you will end up with the original set.
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