Is this definition of overlapping sets correct?
If the intersection of two sets is non-empty set but neither is a subset of the other, the sets are called overlapping sets
It is written in a book. I couldn't make out the last part (i.e neither is a subset of the other) how is it possible? If intersection of two sets has some common elements, then this resulting set will be subset of any of two sets.
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$\begingroup$The "neither is a subset of the other" is not referring to the intersection, but to the two sets themselves. So it is saying that the first set is not a subset of the second, and the second is not a subset of the first.
So, a rewritten definition would be:
$A$ and $B$ are overlapping if $A\cap B\neq \emptyset$ and it is not true that $A\subseteq B$ or $B\subseteq A$.
Under this definition, $\{1,2\}$ and $\{2,3\}$ are overlapping, but $\{1,2\}$ and $\{2\}$ are not, because $\{2\}$ is a subset of $\{1, 2\}$.
This is a good example of how spoken language can be vague and confusing, and a great case for using mathematical symbols for clarity.
$\endgroup$ 3 $\begingroup$Let $A$ and $B$ two sets. If $A \cap B \ne \emptyset$, $A$ is not a subset of $B$ and if $B$ is not a subset of $A$ , then the sets are called overlapping .
$\endgroup$ $\begingroup$Let's call the two sets $A$ and $B.$ What is meant is that the two sets have elements in common ($A\cap B\neq \emptyset$), but $A$ contains elements which are not in $B,$ and $B$ contains elements which are not in $A.$
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