Answer
The set has $7$ elements.
Work Step by Step
A set has $127$ proper subsets.
The formula for the number of proper subsets when the set has $n$ elements is: $2^n-1$.
$2^n-1=127$
$2^n=128$
$2^n=2^7$
$n=7$
The set has $7$ elements.
Thinking Mathematically (6th Edition)
by Blitzer, Robert F.
Published by
Pearson
ISBN 10:
0321867327
ISBN 13:
978-0-32186-732-2
Chapter 2 - Set Theory - 2.2 Subsets - Exercise Set 2.2 - Page 70: 114
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