Let's analyze the given reactions and determine the products $\mathrm{A}$ and $\mathrm{B}$.

Reaction with PCl₃:

When an alcohol ($\mathrm{ROH}$) reacts with phosphorus trichloride ($\mathrm{PCl}_3$), the hydroxyl group ($\mathrm{OH}$) of the alcohol is replaced by a chloro group ($\mathrm{Cl}$), resulting in the formation of an alkyl chloride ($\mathrm{RCl}$). Additionally, the reaction produces phosphorous acid as a byproduct. This can be represented as:

$$3 \mathrm{ROH} + \mathrm{PCl}_3 \rightarrow 3 \mathrm{RCl} + \mathrm{H}_3\mathrm{PO}_3$$

Here, $\mathrm{A}$ is $$\mathrm{H}_3\mathrm{PO}_3$$ (phosphorous acid).

Reaction with PCl₅:

When an alcohol reacts with phosphorus pentachloride ($\mathrm{PCl}_5$), it also replaces the hydroxyl group with a chloro group. The reaction differs slightly in the byproducts; phosphorus oxychloride ($\mathrm{POCl}_3$) and hydrogen chloride ($\mathrm{HCl}$) are produced:

$$\mathrm{ROH} + \mathrm{PCl}_5 \rightarrow \mathrm{RCl} + \mathrm{HCl} + \mathrm{POCl}_3$$

Here, $\mathrm{B}$ is $\mathrm{POCl}_3$ (phosphorus oxychloride).

Thus, in the reactions provided:

• $$\mathrm{A} = \mathrm{H}_3\mathrm{PO}_3$$
• $$\mathrm{B} = \mathrm{POCl}_3$$

Matching these findings against the provided options, we see that Option D correctly identifies $\mathrm{A}$ as $$\mathrm{H}_3\mathrm{PO}_3$$ and $\mathrm{B}$ as $\mathrm{POCl}_3$:

Option D: $$\mathrm{H}_3 \mathrm{PO}_3$$ and $\mathrm{POCl}_3$

This is the correct answer.