Empty Set is a Subset of Every Set

Definition of 'subset' is: A is a subset of B if $x \in A \implies x \in B$
This is an implication statement (If P then Q where P and Q are propositions).
The truth table is Implication Statement is:
P   Q   P=>Q
T   T       T
T   F       F
F   T       T
F   F       T
where T is 'True' and F is 'False'.
That is the truth value of an implication statement is always 'True' when the first proposition (P) is false.
Consider the statement $x \in A \implies x \in B$
Suppose A is an empty set. Then 'x is in A' is false as A contains no element. Hence the implication statement's truth value is True.
Thus A is a subset of B. Since B is any set and A is an empty set, therefore empty set is a subset of any set.