A null set is a subset of other sets I was wondering, how can a null set be a subset of other sets? Could anyone explain the idea in non technical terms, I'm just a beginner. :)
Thank you!
 A: It's a bit tricky.
Suppose you are looking at some set $S$ and you want to know if $\varnothing \subset S$.  So you ask yourself:

Is every element of $\varnothing$ an element of $S$?

You might think that the answer to this question is "No" because $\varnothing$ doesn't have any elements.  But in fact that is precisely the reason that the answer to the question is "Yes".  Because $\varnothing$ has no elements, there aren't any elements in $\varnothing$ that aren't in $S$.  Which is precisely the criterion that you need in order to say that $\varnothing \subset S$.
It might help if instead of defining subset using an affirmative formulation:

$T \subset S$ means that every element of $T$ is also an element of $S$

you instead use the equivalent negative formulation:

$T \subset S$ means that there aren't any elements of $T$ that aren't also elements of $S$.

Edited to add:
Just an afterthought.  If you are new to studying mathematics you might find it helpful to know that this approach -- restating "Property $P$ is always true" as "Property $P$ is never false" -- is a fairly common technique in proving something.  This type of argument is very close to what is known as an indirect proof ("indirect" because of showing that something is true, we show that is can't be false).
A: It is essentially a byproduct of the way we consider it and, also, the way we define implication in classical logic. 
If I say to you: "if it is saturday, I'll take my dog for a walk", you could say I'm lying only if it's saturday and I haven't taken my dog for a walk; that is: an implication $p \Rightarrow q$ is only false when $p$ is true and $q$ is false. If it isn't saturday, it doesn't matter if I take or not take my dog for a walk: I haven't broken my promise.
Now, talking about sets: we say a set $A$ is a subset of another set $B$ when having an element in $A$ implies it must be in $B$. In formal language one would say $A\subseteq B \iff (x\in A \Rightarrow x\in B)$. We take for granted (as an axiom: something we believe is true) that there exists a set $\emptyset$ that has no elements at all (this means that $x\in \emptyset$ is always false). If $x\in \emptyset$ is always false, one could always say, for any set $A$, that $x\in \emptyset \Rightarrow x\in A$ is true, because it's never saturday. As mweiss says, there's not an element in $\emptyset$ that isn't in A, because $\emptyset$ has no elements: we're not breaking the promise. 
A: Here is one way of thinking about it. Let $A$ be an arbitrary set. Suppose the empty set, $\varnothing$, were not a subset of $A$. Then this would mean that $\varnothing$ would contain an element $x$ such that $x \in \varnothing$ but $x \notin A$. But this is impossible since $\varnothing$ does not contain any elements. So $\varnothing$ must be a subset of $A$.
A: I agree with the comment that you should learn the relevant definitions; without them there's no chance of understanding what's going on.  I also recommend that, in connection with learning what it means for $X$ to be a subset of $Y$, you also think about what it means for $X$ not to be a subset of $Y$. You'll find that it means the same as "there is an element of $X$ that isn't in $Y$."  Once you know this, your question is essentially answered.  For $\varnothing$ not to be a subset of your favorite set $Y$ there would have to be an element in $\varnothing$ that isn't in $Y$.  That can't happen, because $\varnothing$ has no elements.  So it's impossible for $\varnothing$ not to be a subset of $Y$. 
A: I have a bag of groceries. In it I have an apple, a pear, a potato and a fig. I'll use set notation to show the contents: {apple, pear, potato, fig}
What bags of groceries can I construct from this?
Well I could put the apple in a bag and get {apple}.
I could put a pear in a bag and get {pear}.
But I could also put an apple and a pear in a bag to get {apple, pear}.
The subsets of the original set (or should I say subbags?) are the sets you can construct using what's in the original set and I've just given three examples of subsets.
Using that definition I could also just put everything back in the back to get {apple, pear, potato, fig}. So that's a subset, even though it's the original set.
And at the other extreme, I could take the bag and leave out the contents. That gives the set {}. By definition, it's a subset. What's more, no matter what groceries I started with the empty set would still be a subset.
