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tema: present perfect simple vs presente perfect continuous ​

Which verb or verb phrase signals an inappropriate shift in mood. a) will you let b) should first change c) must attend d) will be served

Idon't know which one from these two forms is correct! "he believed that the technology of the future would allow robots to do the same tasks as a human." or "he believed that the technology of the future would have allowed robots to do the same tasks as a human. , it's ! i need your !

Which should be added after the sentence 6 to most effectively move a the plot forward