In Exercise 6 in one of the GF2 examples ,In one of the crossings

" ~abc + a~bc + ab~c + abc ↔ (a ⊕ 1)bc ⊕ a(b ⊕ 1)c ⊕ ab(c ⊕ 1) ⊕ abc"

Why was XOR added to each pass between each couple’s connection for example

(a ⊕ 1)bc **⊕** a(b ⊕ 1)c (which is marked in black bold ** **) how we got it?

not(x)=(x xor 1).

The rest is application of the distributive law.