Exercise 1: Why Programs A and C Are Mathematically Identical — Possible Solution
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The disease is expected to affect 600 people in total, in both
framings.

Program A states that 200 people will be saved for certain. If 200 of
600 people are saved, the remaining 600 - 200 = 400 people are not
saved - meaning they die.

Program C states that 400 people will die for certain. If 400 of 600
people die, the remaining 600 - 400 = 200 people do not die - meaning
they are saved.

Both programs therefore describe the exact same real-world outcome:
200 people survive, and 400 people do not. The only difference between
"Program A: 200 saved" and "Program C: 400 die" is which half of the
same fixed total (600 people) the sentence chooses to describe -
whether it names the surviving group or the group that doesn't
survive. The underlying reality being described - who lives and who
dies - is identical in both statements; only the words chosen to
express it differ.

ANSWER: Program A (200 saved) and Program C (400 die) both describe an
identical real outcome out of 600 total people: 200 survive and 400 do
not. Since 600 - 200 = 400, and 600 - 400 = 200, the two programs
simply describe opposite halves of the exact same fixed group - the
actual result is the same regardless of which half is named.

WHY THIS WORKS AS AN ANSWER
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This works through the actual arithmetic connecting the two framings,
proving mathematical equivalence directly rather than only asserting
that the two programs are "the same."