# How would I prove that the regular expression rejects string?

Prove that the regular expression $$\Sigma\Sigma(ab\cup ba)^∗a$$ rejects the string $$aabaabba$$.

Would this be because the union of $$ab$$ and $$ba$$ would not accept the string $$aabaabba$$? I'm just confused on how to explain it.

• I don't know what "ΣΣ" means. Please also use MathJax to type math. – Dmitry Apr 7 at 20:01
• Presumably $\Sigma$ stands for $a \cup b$. – Yuval Filmus Apr 8 at 6:56

Any word accepted by this regular expression has to be either in length 3 or to end with $$aba$$ or $$baa$$.
Try to prove this fact, and use it to show that $$aabaabba$$ must be rejected.
• I think it should be "end with $aba$ or $baa$". – Nathaniel Apr 7 at 19:41