Y = (A ⊕ B) ⊕ (C ⊕ D)
Y = 1, iff A ⊕ B is 1 and C ⊕ D is 0 or, A ⊕ B is 0 and C ⊕ D is 1
=> Y = 1 iff:
1) A = B' and C = D
=> A+B+C+D = 1 or, 3
=> S = 2 or, 4
or,
2) A = B and C = D'
=> A+B+C+D = 1 or, 3
=> S = 2 or, 4
Y = 0, iff A ⊕ B is 1 and C ⊕ D is 1 or, A ⊕ B is 0 and C ⊕ D is 0
=> Y = 0 iff:
1) A = B' and C = D'
=> A+B+C+D = 2
=> S = 2
or,
2) A = B and C = D
=> A+B+C+D = 0 or, 4
=> S = 0 or, 4
=> B)