After residents of an apartment building complain of a weird smell coming from one of the apartments, the brigade of firemen and police break down the door of the apartment in Paris to find the corpse of Anne (Emmanuelle Riva) lying on a bed, adorned with cut flowers.
The film goes back to several months before the opening scene, and Anne and her husband Georges (Jean-Louis Trintignant), both retired piano teachers in their eighties, attend a performance by one of Anne's former pupils, Alexandre. They return home to find that someone has unsuccessfully tried to break in to their apartment. The next morning while they are eating breakfast, Anne silently suffers a stroke. She sits in a catatonic state, not responding to Georges. She comes around as Georges is about to get help, but doesn't remember anything that took place. Georges thinks she was playing a prank on him. Anne is unable to pour herself a drink.
Anne undergoes surgery on a blocked carotid artery, but the surgery goes wrong, leaving her paralyzed on her right side and confined to a wheelchair. She makes Georges promise not to send her back to the hospital or into a nursing home. Georges becomes Anne's dutiful, though slightly irritated, caretaker. One day, Anne tells Georges that she doesn't want to go on living.
Alexandre, her former pupil whose performance they attended, stops by and Anne gets dressed up and carries on a lively conversation during the visit, giving Georges hope that her condition was temporary. However, she soon suffers a second stroke that leaves her demented and incapable of coherent speech. Georges continues to look after Anne, despite the strain it puts on him.
Georges begins employing a nurse three days a week. Their daughter, Eva (Isabelle Huppert), wants her mother to go into care, but Georges says he will not break the promise he made to his wife. He employs a second nurse, but fires her after he discovers she is mistreating his wife.
One day, Georges sits next to Anne's bedside and tells her a story of his childhood, which calms her. As he reaches the story's conclusion, he picks up a pillow and smothers her.
Georges returns home with bundles of flowers in his hands, which he proceeds to wash and cut. He picks out a dress from Anne's wardrobe and writes a long letter. He tapes the bedroom door shut and catches a pigeon which has flown in from the window. In the letter, Georges explains that he has released the pigeon. Georges imagines that Anne is washing dishes in the kitchen and, speechless, he gazes at her as she cleans up and prepares to leave the house. Anne calls for Georges to bring a coat, and he complies, following her out the door.
The film concludes with a continuation of the opening scene, with Eva seated in the living room, after she has wandered around the now-empty home.

Question: Who is Anne and Georges's daughter? 
Answer: Eva
Alternative answer: Eva