Exercise 3.8 (Solution with Regard to Variables). Let be given the function f(x1, . . . , xk, xk+1, . . . , xn).

1 What can be said about the number of solutions of the equation f(x) = 1 if it is required to solve this equation with regard to xk+1(x1, . . . , xk), . . . , xn(x1, . . . , xk).

2 Is the condition formulated with regard to the number of solutions a necessary or a sufficient condition?

3 Use this knowledge in order to decide whether the equation

(x1x4 ∨ x1x2x4 ∨ x1x3x4 ∨ x2x3x4x5) ∧ (x2x3 ⊕ x5) = 1 can be solved with regard to x4(x1, x2, x3) and x5(x1, x2, x3) uniquely.

Verify the solution