Final answer:
Decidable languages are closed under complementation, union, and intersection because a Turing machine can be constructed to accept or reject strings based on these operations.
Step-by-step explanation:
The correct answer is option Computers and Technology. In the context of theoretical computer science, a language is said to be decidable if there exists a Turing machine that can accept all strings in the language and reject all strings not in the language within a finite amount of time. To prove that decidable languages are closed under complementation, consider that if a language L is decidable, its complement L' is also decidable because the Turing machine for L can be modified to accept strings in L' and reject those in L.
For closure under union and intersection, consider two decidable languages L1 and L2 with Turing machines M1 and M2 respectively. To decide the union L1 U L2, construct a Turing machine that simulates both M1 and M2 on a given string; if either accepts, the new machine accepts. For the intersection L1 ∩ L2, the machine accepts a string only if both M1 and M2 accept it. This shows decisively that decidable languages are closed under these operations.