Exercise 3: Mapping Each Worked-System Step to Its Discrete Math Topic — Possible Solution
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STEP 1: THE ACCESS RULE ITSELF, WRITTEN WITH AND/OR/NOT — PROPOSITIONAL
LOGIC (CHAPTER 2)
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The rule combines statements ("is admin," "owns the resource") using
the connectives AND, OR, and NOT, and its negation is derived using
De Morgan's Law - this is propositional logic, working with whole
statements that are true or false, combined by connectives.

STEP 2: "EVERY ADMIN CAN ACCESS EVERY RESOURCE" — PREDICATE LOGIC AND
QUANTIFIERS (CHAPTER 3)
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This statement isn't about one fixed proposition - it makes a claim
about every user and every resource at once, using "every," which is
exactly the universal quantifier. Predicates (Admin(u), CanAccess(u,r))
combined with a quantifier are Chapter 3's own specific territory,
distinct from the fixed, unquantified statements of Chapter 2.

STEP 3: COMBINING VISIBLE RESOURCES WITH UNION — SETS AND SET
OPERATIONS (CHAPTER 4)
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Computing "owned resources combined with admin-visible resources"
using union is a direct set operation on two collections of
resources - Chapter 4's own subject specifically.

STEP 4: OWNERSHIP AND "SAME TEAM AS," ONE OF WHICH IS AN EQUIVALENCE
RELATION — RELATIONS (CHAPTER 5)
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Both "owns" and "is on the same team as" connect pairs of things (a
user to a resource, or a user to another user) - this is a relation.
Checking whether "same team as" satisfies reflexive, symmetric, and
transitive properties to qualify as an equivalence relation is
specifically Chapter 5's own material.

STEP 5: CHECKING THE USER LOOKUP IS INJECTIVE — FUNCTIONS (CHAPTER 6)
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Verifying that no two different users share the same ID - so that a
given ID reliably identifies exactly one user - is checking the
injectivity of a function, exactly Chapter 6's own defining property.

STEP 6: PROVING THE RECURSIVE PERMISSION CHECK CORRECT VIA A BASE CASE
AND INDUCTIVE STEP — PROOF TECHNIQUE AND INDUCTION (CHAPTERS 7-8)
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Establishing correctness for a recursive function across every
possible folder-tree depth, using a base case (the root folder) and an
inductive step (assuming correctness at depth k implies it at depth
k+1), is structural induction - Chapter 8's own subject, building on
Chapter 7's general proof-technique material.

STEP 7: COUNTING 2 x 2 x 2 COMBINATIONS FOR TEST COVERAGE —
COMBINATORICS (CHAPTER 9)
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Multiplying the number of possible states for each of several
independent boolean conditions together to get a total count of
combinations is the multiplication principle - Chapter 9's own
foundational counting rule.

WHY THIS WORKS AS AN ANSWER
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Each step is matched to its topic by identifying the specific
mathematical operation or reasoning pattern actually being used in
that step's own description - quantified claims, set operations,
relation properties, function injectivity, inductive proof structure,
and counting combinations - rather than simply repeating the chapter
numbers already given in the original worked system.