Would anybody . . . . . . . . a mother have risked his or her life for the baby.

The correct answer is: A. rather

The word “rather” is used to introduce a statement that expresses a preference for something over something else. In this case, the speaker is expressing a preference for a mother risking her life for her baby over anyone else doing so.

The other options are not correct because they do not express a preference.

• The word “but” is used to introduce a statement that contrasts with what has been said before. In this case, the speaker would not be contrasting the idea of a mother risking her life for her baby with the idea of someone else doing so.
• The word “however” is used to introduce a statement that qualifies or contradicts what has been said before. In this case, the speaker would not be qualifying or contradicting the idea of a mother risking her life for her baby.
• The word “than” is used to compare two things. In this case, the speaker is not comparing a mother risking her life for her baby to anything else.