Some reactions of NO$$_2$$ relevant to photochemical smog formation are

Identify A, B, X and Y

Photochemical smog formation begins with the photolysis of nitrogen dioxide:

$$NO_2(g) \xrightarrow{\text{Sunlight}} NO(g) + O(g)$$

Comparing this with $$NO_2 \rightarrow X + Y$$:

• $$X = O$$ (nascent oxygen)

• $$Y = NO$$ (nitric oxide)

The nascent oxygen atom then reacts with atmospheric oxygen to form ozone:

$$O(g) + O_2(g) \rightleftharpoons O_3(g)$$

Comparing this with $$X + A \rightarrow B$$:

• $$A = O_2$$

• $$B = O_3$$

Therefore,

$$X = O,; Y = NO,; A = O_2,; B = O_3$$

Hence, the correct answer is:

$$\boxed{\text{Option A}}$$