Exercise 1: A NAT Gateway Route Means Private, Not Public — Possible Solution
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Whether a subnet is public or private is determined entirely by where
its own route table sends internet-bound (0.0.0.0/0) traffic -- not
by anything about the subnet's own configuration otherwise. A route
table that sends 0.0.0.0/0 to an Internet Gateway makes a subnet
public; a route table that sends it to a NAT Gateway instead does
not.

A NAT Gateway only provides real, one-way OUTBOUND internet access --
instances in the subnet can initiate connections out (downloading
updates, calling an external API), but nothing on the internet can
initiate a new connection back IN to those instances, since the NAT
Gateway never exposes them with a real, directly reachable public IP
of their own.

ANSWER: This subnet is PRIVATE, not public, despite having real
internet connectivity. Its instances gain the capability to reach
out to the internet (outbound access for updates, API calls, etc.)
but lack the capability to be reached FROM the internet (no inbound
connections can be initiated by an outside party) -- exactly the
asymmetric behavior the chapter describes as the real, defining
difference between a NAT Gateway and an Internet Gateway.

WHY THIS WORKS AS AN ANSWER
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This correctly applies the chapter's own real rule -- that public vs.
private is decided by the route table's target, not by "does this
subnet have any internet access at all" -- and explains the specific
capability gained (outbound) and lost (inbound) rather than just
asserting the subnet is private without justification.