• Status: Solved
  • Priority: Medium
  • Security: Public
  • Views: 279
  • Last Modified:

regular expression theory [3]

Hello Experts,

I've got two statements concerning theorems about regular expressions:

If L1 is regular, then L1  U  L2 is regular for any language L2.

If L1 and L2 are not regular, then L1 \ L2  [L1 intersection L2]   is not regular.

is any of these statements true ?
if not , can anyone explain me why ?

Thanks in advance for any assistance !
1 Solution
Consider whether the empty language is regular
Look at the properties of Regular Expressions.

- An empty set is a regular expression
- If L1 is regular and L2 is regular, then so is the disjunction, if only L1 is regular then we can't say if L2 is unknown.
- Third, we know that for all a there's an alphabet of symbols

So.. the first statement is only true if L2 is regular, otherwise it is false
The second statement, intersection, the opposite is true, If L1 and L2 are regular than so is L1 \ L2.

Perhaps the following link is useful: http://jonah.cs.elon.edu/sduvall2/courses/csc351/2007spring/Lectures/Prop.ppt

Featured Post

What does it mean to be "Always On"?

Is your cloud always on? With an Always On cloud you won't have to worry about downtime for maintenance or software application code updates, ensuring that your bottom line isn't affected.

Tackle projects and never again get stuck behind a technical roadblock.
Join Now