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Let X be a set (P(X), Δ,∩) where P(X) is the power set of X, and Δ is the symmetric difference. It has unity, and either 1R = ∅ or 1R = X. Figure out which one it is and explain why.

Let X be a set (P(X), Δ,∩) where P(X) is the power set of X, and Δ is the symmetric difference. It has unity, and either 1R = ∅ or 1R = X. Figure out which one it is and explain why.

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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Let X be a set (P(X), Δ,∩) where P(X) is the power set of X, and Δ is the symmetric difference.
It has unity, and either 1R = ∅ or 1R = X. Figure out which one it is and explain why.

Expert Solution
Step 1: Definition used and given.

Unity: Let R, +, ∘ be a ring. If the semi-group R, ∘ has identity element then it is called as unity of a ring R, +, ∘.

Given: P(X), ∆, ∩, where P(X) is a power set of a set X and ∆ is the symmetric difference.

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