Exercise 1: A Script That Starts a Logged, Detached Session — Possible Solution
=================================================================================

start-backup.sh:

  #!/bin/bash
  # Start a detached, logged screen session called "backup".
  cd "$HOME" || exit 1          # screenlog.0 is written here

  screen -dmS backup -L bash -c '
      for i in 1 2 3; do date; sleep 20; done
      echo "Backup finished"
      exec bash                 # keep the window open afterwards
  '

  echo "Started. Check with: screen -ls   or   tail -f ~/screenlog.0"

Run it:

  $ chmod +x start-backup.sh
  $ ./start-backup.sh

Check on it without attaching:

  $ screen -ls                  # shows 12345.backup (Detached)
  $ tail -f ~/screenlog.0       # watch the log fill up (Ctrl-C to stop)

After about a minute the log ends with "Backup finished". Because of
`exec bash`, the window stays open, so you can reattach (screen -r
backup) and read the final output there too. End it with:

  $ screen -S backup -X quit

WHY THIS WORKS AS AN ANSWER
------------------------------
It combines -dmS (detached), -L (logging) and the bash -c ... exec bash
trick, and shows two ways to check progress without attaching. On
newer screen versions, -Logfile ~/backup.log would give the log a
clearer name.