In a short story, the basic situation is really the exposition. The basic situation or exposition introduces the setting of the story, the main characters, and the main conflict.
In "The Cold Equations," the basic situation hints that the story will not end on a positive note. Additionally, the basic situation tells us that the story's resolution will depend upon supposedly immutable laws, laws in which humanity's dictates cannot have a place:
There could be no alternative—but it required a few moments of conditioning for even an EDS pilot to prepare himself to walk across the room and coldly, deliberately, take the life of a man he had yet to meet. He would, of course, do it.
It was the law, stated very bluntly and definitely in grim Paragraph L, Section 8, of Interstellar Regulations: “Any stowaway discovered in an EDS shall be jettisoned immediately following discovery.”
It was the law, and there could be no appeal.
The basic situation introduces us to the main protagonist and antagonist of the story. Barton (the EDS pilot) and Marilyn (the stowaway) are the main protagonists. The antagonist of the story appears to be an immutable law in the Interstellar Regulations: Paragraph L, Section 8. This section of the law dictates that all stowaways must be jettisoned and that no appeals to compassion can be entertained.
The basic situation also tells us that Barton is struggling with an internal conflict and that this conflict is key to the resolution of the story. Basically, Barton does not want to obey the laws he has sworn his allegiance to. So the main conflict here is man versus self. Barton must struggle to reconcile his professional training with his personal ideals.
The basic situation essentially gives us background information about the story. It introduces us to the setting (an EDS cruiser in space), the main characters (Barton and Marilyn), and the main conflict (science versus humanity).