Exercise 1: Deriving the Denial Condition for Admin ^ (Owner v SharedWith) — Possible Solution
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THE STARTING EXPRESSION
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The access rule is: Admin ^ (Owner v SharedWith)
Its negation - the denial condition - is: ~(Admin ^ (Owner v SharedWith))

STEP 1: APPLYING DE MORGAN'S LAW FOR AND
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Per Chapter 2's own De Morgan's Law, ~(p ^ q) = ~p v ~q. Treating
p = Admin and q = (Owner v SharedWith):

  ~(Admin ^ (Owner v SharedWith))
  = ~Admin v ~(Owner v SharedWith)

STEP 2: APPLYING DE MORGAN'S LAW FOR OR TO THE REMAINING TERM
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The inner term ~(Owner v SharedWith) is itself a negated OR. Per
Chapter 2's own De Morgan's Law for OR, ~(p v q) = ~p ^ ~q. Treating
p = Owner and q = SharedWith:

  ~(Owner v SharedWith) = ~Owner ^ ~SharedWith

STEP 3: SUBSTITUTING BACK IN
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Combining both steps:

  ~Admin v (~Owner ^ ~SharedWith)

THE FINAL DENIAL CONDITION
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  ~Admin v (~Owner ^ ~SharedWith)

In plain English: access is denied when the user is not an admin, OR
(they don't own the resource AND it wasn't shared with them). This
reads naturally as the correct denial message: "you're not an admin,
and you neither own this resource nor was it shared with you."

WHY BOTH DE MORGAN'S LAWS WERE NEEDED, NOT JUST ONE
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The original expression has two nested connectives - an outer AND and
an inner OR - so negating it fully requires applying De Morgan's Law
twice: once to flip the outer AND into an OR (per Chapter 2's rule
for AND), and again to flip the newly-exposed inner OR into an AND
(per Chapter 2's rule for OR). Stopping after only the first
application would have left ~(Owner v SharedWith) unsimplified,
still containing a negated compound expression rather than a fully
distributed one.

WHY THIS WORKS AS AN ANSWER
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It applies De Morgan's Law in two separate, clearly labeled steps -
first to the outer AND, then to the newly-exposed inner OR - arriving
at a fully simplified denial condition with no remaining negated
compound expressions, and translates the result into a natural
plain-English denial message.