A few of these here I just wanted to make sure I had right.
For $\Sigma = \{0,1\}$
a. The language consisting of all strings of 0's and 1's that have even length and where 0's and 1's alternate
I got $(10)^* \cup (01)^*$
b. The language consisting of all strings of 0's and 1's with an even number of 1's. Such strings are said to have even parity.
I had $(011)^* \cup (110)^*$
c. And the language consisting of all strings of 0's and 1's that do not contain two consecutive 1's.
I had $(01)^*$
Please say if I'm wrong and why, would help a lot.
a is right.
b is wrong because it doesn't include $0011$. A correct formula is $(0^*10^*1)^*0^*$.
c is wrong because it doesn't include $1010$ or $0010$. A correct formula is $(10 \cup 0)^*$.