A language L is called hereditary if it has the following property:
For every nonempty string x in L, there is a character in x which can be deleted from x to give another string in L.
Prove by contradiction that every nonempty hereditary language contains the empty string.
Here's my attempt:
To prove by contradiction, we assume that for every nonempty string x in L, there is no character in x which can be deleted from x to give another string in L.
This means that if a character in x is deleted an empty string is left. Since an empty string is also a string, every nonempty hereditary language contains the empty string.
I'm not exactly sure how to proof by contradiction. Can someone help review this?