Exercise 2.39. Show that the following systems of functions are complete systems:

1 {x ↓ y};

2 {xy ⊕ z, (x ∼ y) ⊕ z};

3 {x → y, x ⊕ y ⊕ z};

4 {x → y, (1100001100111100)};

5 {0, xy ∨ xz ∨ yz, 1 ⊕ x ⊕ y ⊕ z};

6 {(1011), (1111110011000000)}.