Explanation:

To determine the correct preposition for the sentence "The cat is ________ the chair," we need to consider the relationship between the cat and the chair.

Understanding the sentence:
The sentence is stating the position of the cat in relation to the chair. The cat is positioned in a certain way with respect to the chair.

Options:
Let's analyze each option to determine which preposition fits the sentence.

a) in:
This preposition suggests that the cat is inside the chair, which is not logical or possible. Therefore, option 'a' is not the correct preposition for this sentence.

b) on:
This preposition suggests that the cat is positioned on top of the chair, which is a common and logical position for a cat to be in. Therefore, option 'b' is the correct preposition for this sentence.

c) under:
This preposition suggests that the cat is positioned beneath the chair, which is not mentioned in the sentence. Therefore, option 'c' is not the correct preposition for this sentence.

d) beside:
This preposition suggests that the cat is positioned next to the chair, which is not mentioned in the sentence. Therefore, option 'd' is not the correct preposition for this sentence.

Conclusion:
Based on the analysis, the correct preposition for the sentence "The cat is ________ the chair" is option 'b) on' because it accurately describes the position of the cat on top of the chair.