Exercise 3: Identifying the Correct Set Operation for Each Marketing Request — Possible Solution
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(a) "EVERYONE WHO PURCHASED BUT HASN'T OPTED INTO EMAIL" — P MINUS E
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This asks for people who are in the purchasers set (P) while
specifically excluding anyone also in the opted-in set (E). Per this
chapter's own definition, "difference: A - B = in A, but not in B" is
exactly this - being "in P, but not in E" is precisely P - E, not
E - P (which would instead mean "opted in but didn't purchase," a
different request entirely).

(b) "EVERYONE WHO EITHER PURCHASED, OPTED IN, OR BOTH" — E UNION P
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This asks for anyone who satisfies at least one of the two
conditions, with no restriction against satisfying both. Per this
chapter, "union: A u B = everything in A, B, or both" - the phrase
"or both" in the request is the specific signal that this is a union,
not an exclusive either/or (which would instead be symmetric
difference, E Delta P).

(c) "EVERYONE WHO BOTH PURCHASED AND OPTED IN" — E INTERSECT P
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This asks specifically for people satisfying both conditions
simultaneously - present in both sets at once. Per this chapter,
"intersection: A n B = only what's in both A and B" - the word "both"
in the request is the direct signal pointing to intersection rather
than union.

WHY THE EXACT WORDING IS WHAT DISTINGUISHES THESE THREE REQUESTS
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All three requests involve the same two underlying sets (E and P),
but each uses different qualifying language that maps onto a
different specific operation: "but not" signals difference, "or both"
signals union, and "both" alone signals intersection. Correctly
identifying set operations from a word problem depends on reading
these qualifiers precisely rather than skimming past them.

WHY THIS WORKS AS AN ANSWER
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Each request is matched to its operation by quoting the chapter's own
definition and explaining specifically which words in the request
signal that operation, and by explicitly ruling out the operation's
own "mirror image" (P - E vs E - P; union vs symmetric difference)
where the distinction could otherwise be missed.