# Turing decidable languages

On an old worksheet I came across the question

If L1 and L2 are two Turing decidable languages, then show that 𝐿1∪𝐿2 and 𝐿1𝑜𝐿2 are Turing decidable languages (high-level description with stages is enough).

How do I go about answering this without being given a language to work from?

Both $$L_1$$ and $$L_2$$ are decidable. Hence, they have algorithms $$A_1$$ and $$A_2$$ (respectively) that decide them.
Try to create a new turing machine (algorithm) using the two algorithms $$A_1$$ and $$A_2$$.
For example, for the union $$L_1\cup L_2$$, you can create the following algorithm:
• run $$A_1$$ on the input. If it accepted, then also accept.
• else, run $$A_2$$ on the input, and return what $$A_2$$ returned.
• For each enumeration check if each of the two parts are in $L_1$ and $L_2$ respectively Apr 26 at 22:03