AUTOMATA

Question

L1 → Partially decidable 

L2 -→ Recursively Enumerable

What is 1) L1 U L2 = ?

2. L1 intersection L2 = ? 

Comments

partailly dcidable means semi decidable (if i am not wrong)

semidecidable are RE

and RE are closed under union and intersection so both answers should be RE

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$\text{Semi-Decidable} \iff \text{Partially-Decidable} \iff \text{Recursive Enumerable (REL)} \iff \text{Turing Recognizable} \iff \text{Turing acceptable}$

These terms are interchangable. And REL is closed under Union and Intersection. So, both are closed means both are REL.

Answer 1

L1 :partial decidable = turing recognizable = RE

L2:  RE

RE closed under U and intersection hence result RE