Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 2 - Set Theory - 2.2 Subsets - Exercise Set 2.2: 101

Answer

For an empty set $A$ not to be a subset of a set $B$, there has to be at least one element of $A$ that isn't also an element of $B$, and as $A$ has no elements, there isn't one. Therefore, we can say that the empty set is a subset of every set.

Work Step by Step

For an empty set $A$ not to be a subset of a set $B$, there has to be at least one element of $A$ that isn't also an element of $B$, and as $A$ has no elements, there isn't one. Therefore, we can say that the empty set is a subset of every set. The answer is derived from the definition of an empty set and the definition of a subset.
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