Exercise 3.6 (Implication). There are given the functions f(x) = x1 ⊕

x2 ⊕ x3 ⊕ x4 ⊕ x5 and g(x) = x1x2x3x4x5 ∨ x1x2x3 ∨ x4x5 ∨ x3x5.

1 Check whether f(x) ≤ g(x) holds for the given functions.

2 How the functions f(x) or g(x) must change in order to satisfy the relation f(x) ≤ g(x).

3 Compare the solution sets of f(x) ≤ g(x) and f(x) ∨ g(x) = 1.

4 Compare the solution sets of f(x) ≤ g(x) and f(x)g(x) = 0.