For a given set S, let P(S) be the collection of all subsets of S. Let binary operations + and · on P(S) be defined by A + B = (A ∪ B) − (A ∩ B) and A · B = A ∩ B for A, B ∈ P(S). (c) Prove or disprove that P({x, y} , +, ·) is a commutative ring with unity. (d) Prove or disprove that P({x, y} , +, ·) is an integral domain. (e) Prove or disprove that P({x, y} , +, ·) is a field. can i have help with this few questions algebric structures
For a given set S, let P(S) be the collection of all subsets of S. Let binary operations + and · on P(S) be defined by A + B = (A ∪ B) − (A ∩ B) and A · B = A ∩ B for A, B ∈ P(S). (c) Prove or disprove that P({x, y} , +, ·) is a commutative ring with unity. (d) Prove or disprove that P({x, y} , +, ·) is an integral domain. (e) Prove or disprove that P({x, y} , +, ·) is a field. can i have help with this few questions algebric structures
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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For a given set S, let P(S) be the collection of all subsets of S. Let binary
operations + and · on P(S) be defined by
A + B = (A ∪ B) − (A ∩ B) and A · B = A ∩ B
for A, B ∈ P(S).
(c) Prove or disprove that P({x, y} , +, ·) is a commutative ring with
unity.
(d) Prove or disprove that P({x, y} , +, ·) is an
(e) Prove or disprove that P({x, y} , +, ·) is a field.
can i have help with this few questions algebric structures
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