Chapter 12, Problem 1RQ

Define a Boolean function of degreen.

To determine

To define:

A Boolean function of degree n.

Answer to Problem 1RQ

Let $B=\left\{0,1\right\}$, then $B^n=\left\{\left(x_1,x_2,\mathrm{...},x_n\right)|x_i\in B for 1\le i\le n\right\}$ the Boolean function is of the form of $f:B^n\to B$ i.e., a function from $B^n$ to B is called a Boolean function of degree n.

Explanation of Solution

Let $B=\left\{0,1\right\}$, then $B^n=\left\{\left(x_1,x_2,\mathrm{...},x_n\right)|x_i\in B for 1\le i\le n\right\}$ is the set of all possible n-tuples of 0’s and 1’s. The variable x is called a Boolean variable if it assumes values only from B, that is, if its only possible values are 0 and 1. A function from $B^n$ to B is called a Boolean function of degree n.