Final answer:
The correct answer to the student's question is 'Vanished,' which means to become invisible or disappear, similar to the process of sublimation where a solid becomes gas without passing through the liquid stage.
Step-by-step explanation:
In the given sentence, "She noticed that every time she breathed out, the surface fogged, and she disappeared from her father's table," the correct option is A) Vanished. This means that she became invisible or was no longer visible at her father's table when the surface fogged up as she breathed out. This concept of disappearing or becoming invisible can also relate to how certain solids, through the process of sublimation, transition directly from the solid to the vapor phase without becoming liquid, a scientific phenomenon observable in chemistry and physics. Examples of items that undergo sublimation include dry ice and mothballs, which seem to disappear into the air as they turn into gas.