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During the Elementary OS installation process I checked the "Replace empty disk space" option in the disk encryption settings.
After installation the disk size shows 109 GB free.
Should the disk not show as completely full because of cryptography?
Also, how can I verify that I performed the installation by replacing empty disk space?
Replacing empty disk space just means a full wipe when you re-format a hard disk. It means that sectors are not just marked as empty but also have random noise so that you can't "un-delete" existing files. This doesn't reduce file-system size.
If you look at the Disks utility in applications, you should see at least a a partition table (this shows you the overview of your whole disk), the root partition (the largest normally), and a swap partition.
Now, when you encrypt a disk you will lose space, because your data takes up more space, but that won't reduce the space available on the drive. The total available space is based on the drive itself.
You probably have several GB dedicated to swap (which enables a portion of your disk to function as RAM essentially).
Hopefully this answers your question.
