## Discrete Mathematics with Applications 4th Edition

$L1$is the set of all strings of a’s and b’s that begins with an a and contain only that one a; $L2$ is the set of all strings of a’s and b’s that contain an even number of a’s.
$L1$is the set of all strings of a’s and b’s that start with an a and contain only that one a; $L2$ is the set of all strings of a’s and b’s that contain an even number of a’s. --$L_1L_2$ is the set of all strings of a’s and b’s that begins with an a and contain an odd number of $a’s$. $L1∪L2$ is the set of all strings of a’s and b’s that contain an even number of a’s or that start with an a and contain only that one a. ($L1 ∪ L2$) ∗ is the set of all strings of a’s and b’s. The reason is that a and b are both in $L1 ∪ L2$, and thus every string in a and b is in $(L1 ∪ L2) *$.