## Core Concept
The question tests knowledge of conditions associated with nail involvement. Various systemic and local diseases can affect the nails, leading to changes in their appearance, texture, or structure. Understanding these associations is crucial for diagnosing and managing underlying conditions.

## Why the Correct Answer is Right
Leukemia is a type of cancer that affects the blood and bone marrow. Nail involvement in leukemia can manifest as nail plate changes, such as discoloration, splitting, or brittleness, due to infiltration of leukemic cells into the nail bed or matrix. This association makes option a plausible choice regarding nail involvement.

## Why Each Wrong Option is Incorrect
* **Option A:** Psoriasis is a chronic autoimmune skin condition characterized by rapid skin cell growth leading to thick, red, and scaly patches. Psoriasis commonly affects the nails, causing changes such as pitting, onycholysis (separation of the nail from the nail bed), and subungual hyperkeratosis. Therefore, psoriasis is indeed associated with nail involvement.
* **Option B:** Lichen planus is an inflammatory condition that affects mucous membranes inside the mouth and also the skin. It can cause changes in the nails, including thinning, ridging, and splitting. Lichen planus's association with nail changes makes it an incorrect choice as an exception.
* **Option D:** Sjögren-Larsson syndrome is a rare genetic disorder characterized by congenital ichthyosis, spastic diplegia or quadriplegia, and mental retardation. Skin and nail abnormalities are common, with nail changes including thickening and brittleness. Therefore, this condition is also associated with nail involvement.

## Clinical Pearl / High-Yield Fact
A key point to remember is that while many systemic conditions can lead to nail changes, the specific types of changes can help narrow down the differential diagnosis. For example, pitting of the nails is commonly seen in psoriasis, while onycholysis can be seen in both psoriasis and thyroid disorders.

## Correct Answer: B.