Z is for Zachariah, by Robert C. O’Brien
How the world ends: Nuclear war, classic cold war style
Our protagonist, Ann Burden, survived the war alone in an isolated valley that, through random luck of wind and weather patterns, is one of the few places, maybe the only place, untouched by radiation; her family all died when they went visiting nearby towns looking for other survivors. As far as Ann knows, she may be the only person left living in the entire world. Until, inevitably, another person–a man–shows up, wearing a radiation safe suit made from cutting-edge magnetized plastics.
The characters are also classic cold war characters; the book was written in 1974. Before the war, Ann dreamed of being a teacher, having discarded the one other obvious profession for a teenage girl, nursing. She does all the cooking at first, because the man, John Loomis, is ill, but when the also-inevitable falling out happens, she feels guilty about not continuing to cook his meals. The cooking of meals, and the performing of other domestic chores for herself and the possibly-last-man-in-the-world, is clearly very important to Ann. I couldn’t help but keep thinking of my mother, who for a while kept cooking for my Dad even after she’d announced she wanted a divorce, because cooking for the men in your life, and making sure they had hot meals, was what you did.
But at least our protagonist has also grown used to doing all of the other work of running a farm and generally surviving for herself, too, so when Mr. Loomis–who she always calls by his last name, adding to the book’s dated feel–tries to seize control, she doesn’t go along with it like a well-behaved housewife, but fights for her independence.
Think of it as the end of the world meets the classic early YA problem novel. 🙂