Let $L$ be a regular language. Consider the constructions on $L$ below:
- repeat $(L) = \{ww \mid w \in L\}$
- prefix $(L) = \{u \mid ∃v : uv \in L\}$
- suffix $(L) = \{v \mid ∃u : uv \in L\}$
- half $(L) = \{u \mid ∃v : | v | = | u | \text{ and } uv \in L\}$
Which of the constructions could lead to a non-regular language?
- Both I and IV
- Only I
- Only IV
- Both II and III