examine each of the propositions determine whether or not it is true or not and

Question

examine each of the propositions determine whether or not it is true or not and prove your choice is correct: where Z=integers, N= natural numbers, w= whole numbers

a. w (+,x) is in {rings}

b. (m is in N and (every a, b is in [0] mod m, a*b=ab/m)) ==>[0] mod m (+,*) is in {commutative rings}

c. (m is in N and (every a, b is in [0] mod m, a*b= ab/m)) ==>[0] mod m (+,*) is in {commutative rings with identity}

d. (m is in N and (every a, b is in [0] mod m, a *b = ab/m))==>Z (+,x) is equivalent to [0] mod m (+,*)

Examine each of the following propositions, determine whether or not it is true, display your choice by circling either "T" or "F," and prove that your choice is correct: (Z=integers. N= natural numbers)

Explanation / Answer

1) false as additive inverse not included in w

2)

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