The given statement is: Either $\text{P}$ marries $\text{Q}$ or $\text{X}$ marries $\text{Y}.$
The logical NEGATION of the above statement is : Neither $\text{P}$ marries $\text{Q}$ nor $\text{X}$ marries $\text{Y}.$
We can also write the above statement as $P$ does not marry $Q$ and $X$ does not marries $Y.$
So, the correct answer is $(B).$