This will be an ongoing list for personal reference.
IsaacG - from exercism https://exercism.org/tracks/bash/exercises/hamming/solutions/IsaacG
The && and || in bash are short-circuit logical operators. They quit evaluating as soon as possible.
a && b will only run b if a is true. a || b will only run b if a is false. a || b || c will stop as soon as anything is true. a && b || c will run a and ... b or c or both!! This is why a full blown if-else is often a good idea.
( is a subprocess. The exit status of the subprocess does propagate to the parent shell. If you got set -e (not recommended), you'd get its exit status. But a subshell cannot exit the parent shell.