Exercise 2.41. Represent every function of this exercise using all the complete systems given in Exercise 2.39.

1 f1 = x1 ⊕ x2 ⊕ x3 ⊕ x4 ⊕ x5;

2 f2 = (x1 ∨ x2 ∨ x3)(x1 ∨ x2 ∨ x3) ⊕ x4 ⊕ x5;

3 f3 = (x1 ∨ x2 ∨ x3)(x1 ∨ x2 ∨ x3)(x4 ⊕ x5);

4 f4 = (x1 ⊕ x2 ⊕ x3)(x4 ⊕ x5 ⊕ x6);

5 f5 = (x1 ∨ x2 ∨ x3 ∨ x4 ∨ x5 ∨ x6)(x1 ∨ x2 ∨ x3 ∨ x4 ∨ x5 ∨ x6)?

6 f6 = x2x4x5∨x2x4x5∨(x4⊕x5)(x1x2x3∨x1x2x3)∨x1x2x3(x4 ∼ x5).

7 f7 = (x1 ⊕ x2) ∧ (x3 ∼ x4 ∼ x5).

8 f8 = x1x2 ∨ x2x3 ∨ x3x4 ∨ x4x1.

9 f9 = (x1|x2|x3) ↓ (x4 ↓ x5).

10 f10 = (x1 → x2) ∼ (x2 → x3) ∼ (x3 → x4) ∼ (x4 → x5) ∼

(x5 → x1).