Let T be the set of real numbers. Consider T as an algebraic structure with addition operation and multiplication operation given by x + y = min{x,y}, x©y=x+y - 2. Name the identity element in T for the operation, and prove the inverse law for O. 2 Prove the distributive law in T. [Hint: consider two cases x ≤ y, x > y.] 3 Prove that the set T with addition and multiplication Ⓒ is not a ring.

Let T be the set of real numbers. Consider T as an algebraic structure with addition operation and multiplication operation given by x + y = min{x,y}, x©y=x+y - 2. Name the identity element in T for the operation, and prove the inverse law for O. 2 Prove the distributive law in T. [Hint: consider two cases x ≤ y, x > y.] 3 Prove that the set T with addition and multiplication Ⓒ is not a ring.

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

Let T be the set of real numbers. Consider T as an algebraic structure
with addition operation and multiplication operation given by
xy = min{x,y},
X y = x + y - 2.
Name the identity element in T for the operation, and prove the inverse
law for O.
2 Prove the distributive law in T. [Hint: consider two cases x ≤ y, x > y.]
3 Prove that the set T with addition © and multiplication © is not a ring.

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Step 1: Define ring :-

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Step 2: Explanation of the subpart (1) :-

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Step 3: Explanation of the subpart (2) :-

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Step 4: Continue :-

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Step 5: Explanation of the subpart (3) :-

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I STILL DONT UNDERSTAND HOW YOU GOT 2 AS THE MULTIPLICATIVE INVERSE IN THE FIRST QUESTION

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