In a Boolean algebra with respect to and , denotes the negation of . Then,
and .
Step 1: Explanation for the correct option
For option B : and
The negotiation of a given set is defined as the universal set without the mentioned set.
Thus, the negotiation of set can be given by, .
By the complement law, .
Therefore, and .
So option B is correct.
Step 2: Explanation for the incorrect options
For option A: and .
It is given that, .
It is only valid when, and , as .
Therefore, option (A) is incorrect.
For option C: and .
It is given that, .
Therefore, option (C) is incorrect.
For option D: and .
It is given that, .
It is only valid when, and , as .
Therefore, option (D) is incorrect.
Hence, (B) is the correct option.