Select the appropriate option to complete the following sentence with the correct pair of preposition and pronoun:

Erica York was a self-taught mathematician who liked to spend hours _____ in the library.

by herself

The correct answer is Option (2) → by herself

The completed sentence is: Erica York was a self-taught mathematician who liked to spend hours by herself in the library.

• By herself is an idiomatic phrase meaning alone, without anyone else. This fits the context of a focused, self-taught mathematician dedicating time in a library.

• About herself: Means thinking or talking regarding herself; does not fit the context of spending time alone.

• With her implies the presence of another person, which contradicts the idea of a solitary, focused activity often associated with deep study.

• For herself means for her own benefit or use, which doesn't fit grammatically with the verb "spend hours" and the location "in the library."