[link|http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/karnaugh.html|Karnaugh map]. It's a two dimensional representation of a truth table.
The "sum of products" form is the easiest for filling out Karnaugh maps.
Using your first expression but ignoring the outer negation:
a' a
b' 0 1
b 1 1
negating flips all bits
a' a
b' 1 0
b 0 0
So, indeed it's a'b'.