(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Define apaddockto be a set in which A1 - A4, M1 - M4 and D holds but instead of 1[tex]\neq[/tex] 0, we have 1 = 0. Find an example of a paddock, and show that your example is the only one

2. Relevant equations

A1 - A4, M1 - M4 and D are all axioms

addition axioms

A1: a + b = b + a

A2: (a + b) + c = a + (b + c)

A3: there is a 0 s.t a + 0 = 0 + a = a

A4 for every a there exsist -a s.t a + (-a) = 0

multiplication axioms:

M1: a.b = b.a

M2: (a.b).c = a.(b.c)

M3: there is a 1 s.t a.1 = 1.a = a

M4: for every a there exsist a^{-1}s.t a.a^{-1}= 1

D (a+b)c = ab + bc

a, b, c, 1, 0, inverses all belong in the set

3. The attempt at a solution

the set {1, 0} closed under +_{1}and x_{1}(modulo multiplication of 1 and modulo addition of 1).

1 = 0 because both 0 and 1 are the neutral element,

if it is true how how would i go about showing its the only one. im guessing it requires proof by contradiction.

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# Homework Help: Find feild where 1 = 0 and show that it is the only one

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