Prove that Empty Set is a Subset of Every Set.

Solution :

Let A be any set and \(\phi\) be the empty set.

In order to show that \(\phi\) \(\subseteq\) A, we must show that every element of \(\phi\) is an element of A also. But, \(\phi\) contains no element.

So, every element of \(\phi\) is in A.

Hence, \(\phi\) is the subset of A.