The alphabet is {a, b}. Show that the set of words with the same number of occurrences of a and b is not regular
I am purposefully not going though all the steps required to solve the exercise (comment if you need more help).

You might want to have a look at pumping lemma for regular languages
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It gives you a property that all regular languages must satisfy. If you want to show that a language  $L$ is not regular, you can show that this property cannot hold. In practice, the proof usually follows these steps:


assume towards a contradiction that $L$ is regular
choose a suitable word $w \in L$
apply the pumping lemma on $w$ to conclude that a new word $w'$ must belong to $L$
Use the language definition to show that $w'$ does not belong to $L$ (hence the contradiction). 


Hint:


   Here is a string $w$ that belongs to your language: $a^n b^n$, for a sufficiently large integer $n&gt;0$.