Reduce the following function by using Boolean laws:
F(A, B, C, D) = (A' + C) (A' + C') (A' + B + C'D)

  (A' + C) (A' + C') (A' + B + C'D)  
= (A'A' + A'C' + CA' + CC')(A' + B + C'D) [Distributive Law]  
= (A' + A'C' + A'C + 0)(A' + B + C'D)     [∵ CC' = 0, A'A' = A']  
= [A'(1 + C' + C)](A' + B + C'D)  
= [A'(1 + C)](A' + B + C'D)               [∵ 1 + C' = 1]  
= A'(A' + B + C'D)                        [∵ 1 + C = 1]  
= (A'A' + A'B + A'C'D)                    [Distributive Law]  
= (A' + A'B + A'C'D)                      [∵ A'A' = A'] 
= [A'(1 + B) + A'C'D]     
= [A' + A'C'D]                            [∵ 1 + B = 1]  
= [A'(1 + C'D)]                           [∵ 1 + C'D = 1]  
= A'