For any two languages L₁ and L₂ such that L₁ is context-free and L₂ is recursively enumerable but not recursive, which of the following is/are necessarily true?

I. $${\overline L _1}$$ (complement of L₁) is recursive
II. $${\overline L _2}$$ (complement of L₂) is recursive
III. $${\overline L _1}$$ is context-free
IV. $${\overline L _1} \cup {L_2}$$ is recursively enumerable

Which of the following statements is/are FALSE?

I. XML overcomes the limitations in HTML to support a structured way of organizing content.

II. XML specification is not case sensitive while HTML specification is case sensitive.

III. XML supports user defined tags while HTML uses pre-defined tags.

IV. XML tags need not be closed while HTML tags must be closed.

Which of the following combinations is incorrect?

The given statement is followed by some courses of action. Assuming the statement to be true, decide the correct option.

Statement:
There has been a significant drop in the water level in the lakes supplying water to the city.

Course of action:
(I) The water supply authority should impose a partial cut in supply to tackle the situation.
(II) The government should appeal to all the residents through mass media for minimal use of water.
(III) The government should ban the water supply in lower areas.