Suppose $h$ is the homomorphism from the alphabet $\{0,1,2\}$ to the alphabet $\{a,b\}$ de fined by$:$ $h(0)=a;h(1)=ab,$ and $h(2)=ba.$
- What is $h(0120)?$
- What is $h(21120)?$
- If $L$ is the language $L(01^{*}2),$ what is $h(L)?$
- If $L$ is the language $L(0+12),$ what is $h(L)?$
- Suppose $L$ is the language $\{ababa\}$ that is the language consisting of only the one string $ababa.$ What is $h^{-1}(L)?$
- If $L$ is the language $L(a(ba)^{*}),$what is $h^{-1}(L)?$
