For some reason I can't wrap my head around this one...

I am supposed to use truth tables to explain expressions like

x ⊕ 1 = x

x ⊕ 1 = xnot

x ⊕ 0 = x

etc, etc.

Obviously I can do something like

x

x ⊕ 1

0 1

1 0

but that seems redundant and doesn't really explain how I came to that conclusion. Is there anyway I can expand this truth table to make it clear how I came my conclusion? Any help would be appreciated, thanks!