Inductive reasoning means to get to a generalization out of a single case. If you have been given ONE burnt hamburger and you think that ALL THE FOOD you ordered will also be burnt, you have analysed the situation inductively. Have a look at the language being used:ONE stands for a single case and ALL stands for a universal idea, that is to say; a generalization. The univese in this case is all the food you ordered in that restaurant. If one item from that universe is burnt, all the elements from that universe will be.
The speaker admires and appreciates the librarian. She remembers the librarian's friendliness and how much effort she would make to provide the speaker with the books she wanted. These books were very meaningful and important to the speaker.