MathDB

A subset

W

of the set of real numbers is called a ring if it contains

1

and if for all

a,b\in W

, the numbers

a-b

and

ab

are also in

W

. Let

S=\left\{\frac m{2^n}|m,n\in\mathbb Z\right\}

and

T=\left\{\frac pq|p,q\in\mathbb Z,q\text{ odd}\right\}

. Then

<span class='latex-bold'>(A)</span>~\text{neither }S\text{ nor }T\text{ is a ring}

<span class='latex-bold'>(B)</span>~S\text{ is a ring, }T\text{ is not a ring}

<span class='latex-bold'>(C)</span>~T\text{ is a ring, }S\text{ is not a ring}

<span class='latex-bold'>(D)</span>~\text{both }S\text{ and }T\text{ are rings}

Problem Statement