prove the following propositions #5

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A1:- Commutativity of Addition
A2:- Associativity
A3:- Additive Inverse
A4 :- Identity
A5 :- Commutativity of Multiplication
A6:- Associative
A7 :- Identity of Multiplication
A8 : - Multiplicative Inverse
A9 : - Distributive law
A10 : - Trichotomy
A11: - Transitivity
A12 : - Addition Preserves Order
A13 : -
A14 : - Well ordering property

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