Given:
((ab'+ab)'c + a(b+ab'))'
((ab'+ab)'c + ab+aab')'
((ab'+ab)'c + ab+ab')'.......(a.a = a)
((ab'+ab)'c + a)'...............a(b+b')=a since b+b'=1
((a'+b)(a'+b')c + a)'...........DeMorgan's Law
(a'c+a'b'c+ba'c+bb'c+a)'
(a'c +a'c+a)'.....................a'cb+a'b'c=a'c
(a'c+a)'..................................a+a'b=a+b
(a+c)'
a'c'.................................Answer