Choose the pair that shows the same relationship as the given pair: BRISTLE : BRUSH.

Introduction / Context:
This analogy question tests understanding of part and whole relationships. You are given the pair Bristle and Brush and asked to select a pair that stands in the same relation from the options. Such questions are common in verbal reasoning and help evaluate ability to see structural relationships between objects.

Given Data / Assumptions:
1) A brush is a tool that consists of many bristles fixed to a handle or base.
2) A bristle is one of the stiff hairs or fibres that together make up the working part of the brush.
3) The options are arm : leg, key : piano, recline : chair, and stage : curtain.
4) The correct answer should relate a part and the object made up of many such parts in a similar way.

Concept / Approach:
The relationship in the model pair is that of component to whole. A single bristle is a single element of the larger object, the brush. Many bristles together form the useful surface of the brush. Therefore, in the correct option, the first word should be a small element, and the second word should be the larger object that consists of many such elements.

Step-by-Step Solution:
Step 1: Express the model pair as a sentence. Bristles are parts of a brush. Step 2: Examine option a, arm : leg. Both arm and leg are body parts, but neither is a part of the other. This is a pair of similar category items, not one part of the other. Step 3: Examine option b, key : piano. A piano is a musical instrument that has many keys, and the keys are essential parts of it. Step 4: Examine option c, recline : chair. Recline is a verb meaning to lean back. It is not a physical part of a chair. Step 5: Examine option d, stage : curtain. A curtain hangs in front of a stage, but the stage is not a part of the curtain nor vice versa. They are separate objects placed together. Step 6: Only key : piano shows the same part to whole structure as bristle : brush, where many keys form a key board on the piano just as many bristles form the working part of a brush.

Verification / Alternative check:
Rephrase the correct pair in the same style. Bristles are parts of a brush. Keys are parts of a piano. Both sentences are structurally parallel. This confirms that option b matches the required relationship. No other option gives the same clear part to whole connection.

Why Other Options Are Wrong:
Arm : leg has a relationship of similarity but not composition; neither is made from the other. Recline : chair pairs an action with an object and does not show a part to whole link. Stage : curtain pairs two separate items used in a theatre but again one is not physically made from repeated units of the other.

Common Pitfalls:
One common error is to focus only on whether the two things are often seen together, as in stage and curtain, rather than checking whether one is a physical part of the other. Always ask whether many units of the first thing form the second thing. This test quickly reveals that only key and piano behave like bristle and brush.

Final Answer:
The pair that shows the same relationship as BRISTLE : BRUSH is key : piano.