Difference between membership and inclusion I've taken the definition of membership to be the following:
Membership $A \in B: A$ is one of the members of $B$.
However, I'm not sure where to make the distinction between membership and inclusion, and hence I can't wrap my head around the solutions to the following questions:
"Say whether the following are true or false"
h. $\{2\}\in\{x:x$ is a number between $1$ and $9\}$  (False)
i. $\{2\}\subseteq\{x:x$ is a number between $1$ and $9\}$   (True)
and similarly,
n. $\emptyset\subseteq\{a,b,c\}$ (True)
o. $\emptyset\in\{a,b,c\}$ (False)
I am not sure why (h) and (o) are false but (i) and (n) are true, i.e. I don't see how the same element can be a subset but not a member of the same set.
Is it possibly because membership is only valid between an element and a set rather than a set and a set, while inclusion is valid between a set and a set?
I would appreciate any help in clarifying this, thank you.
 A: $\{2\}$ and $2$ are entirely different things.
$\{2\}$ is a set that has $2$ as its only element-- it is a set and it is not a number.  And $2$ is a number-- it isn't a set.
What are the members of $\{x: x$ is number between $1$ and $9\}$?  Well those members are: $1,2,3,4,5,6,7,8,9$.  Are any of them the same thing as $\{2\}$?  Nope.  Not a single one of those numbers between $1$ and $9$ is the set with $2$ as its only element.  So $\{2\}\not \in \{x: x$ is number between $1$ and $9\}$.  
Are any of those members the same thing as $2$; the number $2$?  Yes, $2$ is the same thing as $2$.  So $2 \in  \{x: x$ is number between $1$ and $9\}$
Is $\{2\}$ a subset of $\{x: x$ is number between $1$ and $9\}$?  Well, is $\{2\}$ a set?  Yes.  What are its members?  Its member is $2$.  What are the members of $\{x: x$ is number between $1$ and $9\}$?  They are $1,2,3,4,5,6,7,8,9$.  Are all of $2$ in the list $1,2,3,4,5,6,7,8,9$?  Yes, it is.
So $\{2\}\subset \{x: x$ is number between $1$ and $9\}$.
Is $2$ a subset of  $\{x: x$ is number between $1$ and $9\}$?  Well, is $2$ a set? No, it is not.  What are its members?  It's not a set; it doesn't have any members. 
So $2 \not \subset \{x: x$ is number between $1$ and $9\}$.
.....
"how the same element can be a subset"  
An element can not be a subset at all.
$\{2\}$ is not an element of $\{x: x$ is number between $1$ and $9\}$
A: Take a look at these examples
$$2\in \{1,3,2\} $$
$$\{2\}\in \{\{1\},\{3,4\},\{2\}\} $$
$$\emptyset\in \{\{3,5\},\emptyset\} $$
a set belongs to a set of sets.
a set is included in a set which contains its elements.
A: Inclusion: If all objects inside set A are also inside set B, $A \subset B$.
Membership: If set/object A is itself inside set B, $A \in B$.
For example, let $A= \{1, 2, 3, 4, 5\}$. 
$A \subset \{1, 2, 3, 4, 5, 6\},$
while $A \in \{\{1, 2, 3, 4, 5\}, 1, 2, 3\}$ (this could also be written $A \in \{A, 1, 2, 3\}).$
(Now... what can we say about $A$ and the set $\{\{1, 2, 3, 4, 5\}, 1, 2, 3, 4, 5\}?)$
