what does $a^* \cup b^*$ mean?

Question

I have to provide a DFA for the following language: $L=\{w|w$ is any string not in $a^* \cup b^*\}$

what does $a^* \cup b^*$ mean?

Answer 1

$\cup$ is the usual set union symbol. $a^*$ is the set $\{ \epsilon, a, aa, aaa, \dots\}$; $b^*$ likewise is $\{ \epsilon, b, bb, bbb, \dots\}$. The union is $\{ \epsilon, a, aa, aaa, \dots, b, bb, bbb, \dots\}$.