Question 1.State whether True or False. Provide a reason in each case.(a) The pair (Z321,-) that consists of the set of congruence classes modulo 321 together withmultiplication, has two zero divisors.(b) Every integral domain consists of an Abelian additive group, and a commutative unitalring which has a unity, but no zero divisors.(c) The set nz for n N, the set R\Q, and the set C\R have no zero divisors.(d) Given the set Z24 of congruence classes modulo 24. Then the congruence classes [2], [3], [4],[6], [9], [12], [18], and [20] are some of the zeros divisors of Z24.(e) The triple (Z[√-3], +,-) consisting of the set of algebraic numbersZ[√-3] = {+ + √-3: for k, l, m, n € Z and I, n ‡ 0}with operations of addition + and multiplication, constitutes an integral domain.(f) The set of all functions M ([0,1]) from the the closed unit interval [0, 1] onto [0, 1],together with usual function addition and function multiplication, does not have any zerodivisors. If you think it does, then give an example.

Answered: Image /qna-images/answer/cf3d7b58-106b-4155-a26c-d22c79f0af63.jpg

Question 1. State whether True or False. Provide a reason in each case. (a) The pair (Z321.-) that consists of the set of congruence classes modulo 321 together with multiplication, has two zero divisors. (b) Every integral domain consists of an Abelian additive group, and a commutative unital ring which has a unity, but no zero divisors. (c) The set nZ for n € N, the set R\ Q. and the set C\R have no zero divisors.

Question 1. State whether True or False. Provide a reason in each case. (a) The pair (Z321.-) that consists of the set of congruence classes modulo 321 together with multiplication, has two zero divisors. (b) Every integral domain consists of an Abelian additive group, and a commutative unital ring which has a unity, but no zero divisors. (c) The set nZ for n € N, the set R\ Q. and the set C\R have no zero divisors.

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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